All publications

We study how SL(2,Z) transformations act on pole-truncated linear-response effective theories in (2+1) dimensions. For correlators meromorphic within a finite low-frequency domain, the EFT data include both derivative-expanded transport coefficients and the retained non-hydrodynamic poles. Since the S-transformation inverts the optical conductivity and exchanges its poles and zeros, it does not necessarily commute with the infrared truncation. We derive explicit maps for static susceptibilities, the Einstein relation and AC transport coefficients. In the purely hydrodynamic sector the map closes on the original transport data, while in quasihydrodynamic regimes the transformed pole positions and, in general, residues constitute additional infrared data. We test the construction in the alternatively quantised D3/D5 probe-brane system, where an EFT retaining one original gapped pole can correspond to transformed EFTs retaining zero, one or two. The holographic results verify the analytic maps and exhibit an inverse-Drude conductivity at large values of the control parameter.

Retarded thermal correlators, analytically continued to complex frequency, exhibit non-hydrodynamic poles and branch cuts that constrain hydrodynamics. We construct Gaussian Schwinger-Keldysh effective actions in which branch cuts arise from continua of relaxation poles and response functions are governed by Stieltjes transforms of relaxation-time densities. Dynamical KMS symmetry, positivity and stability constrain the spectra, while endpoint behaviour controls the local branch structure and near-edge pole scaling. The illustrative examples of uniform and power-law densities exhibit respectively beyond-all-orders pole-endpoint separation and a continuous interpolation between pole-pole and pole-branch-point termination. Finally, we show that an energy-dependent relaxation-time approximation in kinetic theory provides a microscopic realization of our branch cuts at zero momentum.

We determine the conditions under which the nonlinear Maxwell-Cattaneo theory of charge transport admits a local Gaussian Schwinger-Keldysh embedding with a particular modified dynamical KMS symmetry. We show that treating the additional vector as intrinsically dissipative fundamentally modifies the entropy-current analysis: the hydrostatic generating functional no longer fixes all entropy-current improvements, which must instead be supplied independently. Subsequently we discuss the additional constraints not contained in the hydrodynamic analysis that are imposed by the modified KMS transformation becoming a symmetry of the action. We both interpret and supply the corresponding stochastic quasi-hydrodynamics.

Modern effective field theories of dissipative hydrodynamics, built on the Schwinger-Keldysh formalism, include thermal noise that is not Gaussian. The resultant higher-order noise vertices are constrained by symmetries, but otherwise treated as free parameters. We show explicitly that symmetry constraints alone do not guarantee these vertices yield a genuine probability distribution. Requiring a probability interpretation yields sharp bounds between cumulants that are invisible to the symmetry analysis. The bounds are optimal: their boundaries are attained by explicit positive distributions, and constructive completions are provided for both negative- and positive-kurtosis noise data. This gives closed-form nonlinear response and an exact sampling algorithm, whose Monte Carlo implementation reproduces the exact cumulants and nonlinear fluctuation-dissipation relations. Confronted with microscopic results, the framework places a sharp lower bound on the time step required for a positive stochastic completion of a quartic model of the Brownian particle used in the literature, while holographically computed SU(2) noise vertices pass a nontrivial continuum fourth-order positivity test.

We consider the problem of writing an effective, linearised theory in small derivatives that reproduces the Mittag-Leffler expansion of a charge current correlator with an arbitrary number of simple poles. We demonstrate how such a framework can be compatible with hydrostaticity without modification of thermodynamics, properly accounts for the differing notions of smallness in time and space derivatives including setting the lowest order effective equation of motion, and corrects the effective equations in derivatives. As an application, we apply the results to charge fluctuations of the D3/D5 probe brane and quantify how the transport coefficients behave when quasihydrodynamics emerges at large charge density.

We explore new infrared dualities in (2+1)-dimensional quantum field theories involving Majorana fermions. Building on the recently proposed operator-deformation approach to bosonization dualities, we incorporate the bosonization of neutral fermions into the established web of Dirac dualities. Starting from the decomposition of a Dirac fermion into two Majorana components, we derive a hierarchy of dual bosonic descriptions based on orthogonal Chern-Simons-matter theories. This construction leads to novel boson-boson dualities, including an explicit correspondence between an SO(N) theory with two real scalars and a U(1) theory with one complex scalar, and their generalizations to arbitrary numbers of Majorana flavours. We analyze boundary conditions preserving chirality and demonstrate their role in matching gravitational anomalies and chiral central charges. Additional deformations yield orthogonal analogues of Ising-Gross-Neveu and pairing transitions. The resulting framework provides a unified Majorana-based extension of the three-dimensional duality web and clarifies the infrared structure of non-Abelian bosonization.

We develop Hamiltonian mechanics on Aristotelian manifolds, which lack local boost symmetry and admit absolute time and space structures. We construct invariant phase space dynamics, define free Hamiltonians, and establish a generalized Liouville theorem. Conserved quantities are identified via lifted Killing vectors. Extending to kinetic theory, we show that the charge current and stress tensor reproduce ideal hydrodynamics at leading order, with the ideal gas law emerging universally. Our framework provides a geometric and dynamical foundation for systems where boost invariance is absent, with applications including condensed matter, active matter and optimization dynamics.

This note provides a comprehensive examination of the various approaches to formulating relativistic hydrodynamics, with a particular emphasis on the canonical approach. Relativistic hydrodynamics plays a crucial role in understanding the behavior of fluids in high-energy astrophysical phenomena and heavy-ion collisions. The canonical approach is explored in detail, highlighting its foundational principles, mathematical formulations, and practical implications in modeling relativistic fluid dynamics. Following this, we delve into linear response theory, elucidating its relevance in the context of hydrodynamics. We analyze the response of relativistic fluids to external perturbations, discussing the theoretical framework and key results. This dual focus aims to bridge the gap between theoretical foundations and practical applications, offering a robust perspective on the dynamic interplay between relativistic hydrodynamics and linear response theory.

We consider entropy generating flows for fluids that achieve a steady state in the presence of a driving electric field. Having chosen one among the space of stationarity constraints that define such flows we show how energy and momentum relaxation are related in the presence of dissipation. Furthermore, we find that if such a fluid obeys Onsager reciprocity then the incoherent conductivity must be identically zero and consequently makes no contribution to the observable AC or DC charge conductivities.

We use advances in the formalism of boost agnostic passive fluids to constrain transport in polar active fluids, which are subsequently described by the Toner-Tu equations. Acknowledging that the system fundamentally breaks boost symmetry we compel what were previously entirely phenomenological parameters in the Toner-Tu model to satisfy precise relationships among themselves. Consequently, we propose a thermodynamic argument to determine the exact scalings of the transport coefficients under dynamical renormalisation group flow. These scalings perfectly agree with the results of recent state-of-the-art numerical simulation and experiments.

The capability of hydrodynamics to accurately describe slow and long-wavelength fluctuations around non-equilibrium steady states, characterized by a stationary flow of energy or matter in the presence of a driving force, remains an open question. In this study, we explicitly construct a hydrodynamic description of electrically driven non-equilibrium charged steady states in the limit in which the relaxation of the first non-hydrodynamic excitation is parametrically slow. Our approach involves introducing gapped modes and extending the effective description into a relaxed hydrodynamic theory. Leveraging gauge-gravity duality as a tool for controlled computations within non-equilibrium systems, we establish an ultraviolet complete model for these steady states that confirms the validity of our relaxed hydrodynamic theory. Our findings provide a concrete realization of the validity of hydrodynamics beyond thermal equilibrium.

We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare novel lattice simulations for theories with N=3 and 6 color charges, and report an improved estimate for N=2, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. We also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding excellent agreement between lattice results and conformal-perturbation predictions for the three-state Potts model in two dimensions.

We consider as a model of Weyl semimetal thermoelectric transport a (3+1)-dimensional charged, relativistic and relaxed fluid with a U(1)V × U(1)A chiral anomaly. We take into account all possible mixed energy, momentum, electric and chiral charge relaxations, and discover which are compatible with electric charge conservation, Onsager reciprocity and a finite DC conductivity. We find that all relaxations respecting these constraints necessarily render the system open and violate the second law of thermodynamics. We then demonstrate how the relaxations we have found arise from kinetic theory and a modified relaxation time approximation. Our results lead to DC conductivities that differ from those found in the literature, opening the path to experimental verification.

In hydrodynamics, for generic relaxations, the stress tensor and U(1) charge current two-point functions are not time-reversal covariant. This remains true even if the Martin-Kadanoff procedure happens to yield Onsager reciprocal correlators. We consider linearised relativistic hydrodynamics on Minkowski space in the presence of energy, U(1) charge and momentum relaxation. We then show how one can find the minimal relaxed hydrodynamic framework that does yield two-point functions consistent with time-reversal covariance. We claim the same approach naturally applies to boost agnostic hydrodynamics and its limits, including Carrollian, Galilean and Lifshitz fluids.

We show that literature results claimed for the magnetic field dependence of the longitudinal conductivity in anomalous first-order hydrodynamics are frame dependent at this derivative order. In particular, we focus on (3+1)-dimensional hydrodynamics in the presence of a constant first-order magnetic field with a U(1) chiral anomaly and demonstrate that, for constitutive relations up to and including order one in derivatives, the anomaly drops out of the longitudinal conductivity. Magnetic-field-dependent terms previously found in the literature only enter the non-zero-frequency thermoelectric conductivities through explicitly frame-dependent pieces, indicating that they are not physical. This issue can be avoided entirely by incorporating the magnetic field into the fluid's equilibrium state.

Existing hydrodynamic models of charged fluids consider any external electric field acting on the fluid as either first order in the hydrodynamic derivative expansion and completely arbitrary or zeroth order but constrained by the fluid's chemical potential. This is in tension with experiments on charged fluids, where the electric field is both zeroth order and completely arbitrary. We introduce a new class of hydrodynamic stationary states, including an arbitrary zeroth-order electric field, upon which hydrodynamics can be built. We first write down the hydrostatic constitutive relations for a boost-agnostic charged fluid up to first order in derivatives, then introduce suitable energy and momentum relaxation terms to balance the influence of the electric field. This leads to a new hydrostatic constraint on the spatial fluid velocity and to non-trivial thermo-electric transport even at ideal order, with non-zero DC electric and heat currents. We derive the corresponding conductivities and show they depend non-linearly on the electric field.

We use a Ginzburg-Landau approach to show that a suitably strong electric field can drive a phase transition from a superconductor to a normal metal. The transition is induced by taking into account corrections to the permittivity due to the superconductive gap and persists even when screening effects are considered. We test the model against recent experimental observations in which a strong electric field has been observed to control the supercurrent in superconducting thin films. We find excellent agreement with the experimental data and are able to explain several observed features. We additionally suggest a way to test our theoretical proposal via superconductor-superconductor electron tunneling.

A static electric field has traditionally been thought to play little role in ideal conductors because screening by mobile carriers prevents it from penetrating deep into a metal. Recent experiments, however, indicate that static electric fields can manipulate the superconductive properties of metallic BCS thin films and weaken the critical current. This contribution discusses possible explanations for this effect using the analogy between superconductivity and quantum electrodynamics noted by Nambu and Jona-Lasinio.

We review recent progress on relativistic hydrodynamics in (2+1) dimensions with an external magnetic field. We discuss the formalism allowing for momentum loss due to the explicit and spontaneous breaking of translation invariance by scalar operators. We also compare to some results from the gauge/gravity correspondence.

Animal behavior and neural recordings show that the brain can measure both the intensity of an odor and the timing of odor encounters, but which is more informative for olfactory-driven behavior is not understood. We study the problem of locating a target using the odor it releases, feeding data from accurate numerical simulations of odor transport to machine-learning algorithms that learn how to connect odor to target location. We find that both intensity and timing can separately predict target location even from several meters away, although their efficacy varies with spatial dilution. Organisms using olfaction over different ranges may therefore need to switch among different modalities. We also demonstrate simple strategies to improve prediction accuracy and robustness by modifying odor sampling and combining distinct measures.

We study the effective string describing the infrared dynamics of SU(2) Yang-Mills theory in three dimensions. By combining high-precision lattice simulations of Polyakov-loop correlators at temperatures near deconfinement with analytical constraints from renormalization-group arguments, exact integrability of the two-dimensional Ising model, conformal perturbation theory and Lorentz invariance, we derive tight quantitative bounds on corrections to the effective string action beyond the Nambu-Goto approximation. These corrections are compatible with predictions from a bootstrap analysis of the effective string theory, but their value does not allow the Axionic String Ansatz to be established for this model.

We employ hydrodynamics and gauge/gravity to study magneto-transport in phases of matter where translations are broken pseudo-spontaneously. First we provide a hydrodynamic description of systems where translations are broken homogeneously at nonzero lattice pressure and magnetic field, allowing analytic expressions for all relevant transport coefficients. We then construct holographic models of those phases and determine all DC conductivities in terms of the dual black-hole geometry. Combining the descriptions gives analytic expressions for AC thermo-electric correlators, fixed by the black-hole geometry and a numerically determined pinning frequency. We find excellent agreement between hydrodynamic and holographic descriptions and show that the holographic models are good avatars for magneto-phonons.

Near the deconfinement transition, the interquark potential can be predicted precisely using effective string theory. If the transition is continuous, effective-string results can be combined with conformal perturbation theory to detect corrections beyond the Nambu-Goto approximation. For SU(2) gauge theory in (2+1) dimensions we use high-precision simulations to show that the Polyakov-loop correlator is described by the spin-spin correlator of the two-dimensional Ising model from the critical point down to temperatures around 0.8 Tc. Exact integrability extends the comparison beyond the conformal-perturbation regime, allowing us to quantify the first effective-string correction beyond Nambu-Goto and show compatibility with bootstrap bounds.

We study the dynamical properties of charged systems in an external magnetic field and perturbed by scalar operators breaking translations either spontaneously or pseudo-spontaneously. By combining hydrodynamic and quantum field theory arguments we provide analytic expressions for all hydrodynamic transport coefficients relevant for the diffusive regime in terms of thermodynamic quantities and DC thermo-electric conductivities, including the momentum dissipation rate. We clarify the role of momentum dissipation in the transition between pseudo-spontaneous and purely explicit regimes and several relations among transport coefficients observed in holographic charge-density-wave models.

We consider magnetohydrodynamics with an external magnetic field. We find that in general one must allow for a non-zero incoherent Hall conductivity to correctly describe the DC longitudinal and Hall thermal conductivities beyond leading order in the magnetic-field expansion. We apply the result to the dyonic black hole, determine the incoherent Hall conductivity in that case, and show that its existence leads to a significantly better match between hydrodynamic and AC thermo-electric correlators.

We consider the three-dimensional Ising model perturbed by the energy operator coupled to a non-uniform harmonic potential acting as a trap, and show that the system satisfies trap-size scaling. We compute spin-spin, energy-energy and spin-energy correlators near the critical point using conformal perturbation theory. Combining these results with Monte Carlo simulations, we estimate several OPE coefficients and find good agreement with independently obtained values.

A deep connection has long linked superconductivity and quantum field theory, notably through the Anderson-Higgs mechanism and similarities between Dirac and Bogoliubov-de Gennes equations. We extend this parallel and predict a superconducting Schwinger effect: an electrostatic field can generate two coherent excitations from the superconducting ground-state condensate. Unlike dissipative thermal excitations, these form a macroscopically coherent and dissipationless state. We discuss how the superconducting state is weakened by these excitations and how the effect could be tested experimentally, illuminating the interaction between superconductors and electric fields.

High-temperature superconductors are strongly coupled systems with complicated phase diagrams and singular transport properties. Hydrodynamics, relying largely on symmetry rather than a particular microscopic mechanism, provides a promising framework. We show that in the strange-metal phase of cuprates, a set of transport coefficients is described by a universal hydrodynamic framework once quantum-critical charge-density-wave effects are included. We corroborate the prediction by measuring DC transport properties of Bi-2201 close to optimal doping, providing a consistency check on the universality class governing high-temperature cuprate superconductors.

These notes are based on lectures on holographic techniques applied to condensed-matter physics. After introducing the basic holographic dictionary, they analyze a holographic model with spontaneously or pseudo-spontaneously broken translations, providing a holographic realization of a charge density wave. The notes include computations, in particular a derivation of Ward identities, intended as a practical exercise for readers learning advanced techniques for bottom-up holographic models.

We study a holographic model where translations are both spontaneously and explicitly broken, leading to pseudo-phonons in the spectrum. Weak explicit breaking arises from a small source for the condensate and additional linearly space-dependent marginal operators. The low-energy dynamics is described by Wigner-crystal hydrodynamics. Without a source for the condensate the phonons remain gapless while momentum relaxes; turning on a source damps and pins them. We verify that the universal relation between phonon damping rate, mass and diffusivity continues to hold for sufficiently weak explicit breaking.

We uncover a universal relaxation mechanism of pinned density waves using gauge/gravity duality and effective field theory. When translations are spontaneously broken, phonons emerge; weak explicit breaking pins them with a mass and damps them at a computable rate. We show that the damping rate is controlled by the shear modulus, pinning mass and a diffusivity of the purely spontaneous state. At low temperature the collective modes relax quickly into the heat current, so late-time transport is dominated by thermal diffusivity. The resulting resistivity is linear in temperature and the AC conductivity exhibits a transfer of spectral weight from a pinning peak to a Drude-like peak, with possible relevance to cuprate strange metals.

In phases where translations are spontaneously broken, gapless phonons mix at long wavelengths with fluctuations of conserved densities. This mixing is captured by new diffusive transport coefficients and collective modes such as shear sound. Using gauge/gravity duality we model such phases and compute the corresponding diffusivities from black-hole background data. In holographic quantum-critical low-temperature phases we show that these diffusivities are governed by universal relaxation of phonons into the heat current when the dynamical critical exponent exceeds two. We also compute transverse collective modes and find agreement with the shear-sound dispersion of hydrodynamic crystalline solids.

We study the accuracy and predictive power of conformal perturbation theory by comparing with lattice results near the finite-temperature deconfinement transition of SU(2) Yang-Mills theory, assuming its infrared properties near criticality are described by the Ising model. The comparison shows that conformal perturbation theory yields quantitatively accurate predictions over a broad temperature range. We discuss implications for the critical point in another strongly coupled, non-supersymmetric non-Abelian gauge theory: the critical endpoint in the QCD phase diagram at finite temperature and quark chemical potential.

We use gauge/gravity duality to construct an effective low-energy holographic theory of charge density waves. A simple gravity model breaks translations spontaneously and homogeneously in the dual field theory, capturing phonons coupled to conserved currents. Including subleading quartic derivative terms produces dynamical instabilities of translation-invariant AdS2 states and stable phases with spontaneous translation breaking. We compute the real part of the electric conductivity and construct Lifshitz-like hyperscaling-violating quantum-critical ground states whose DC conductivity can be metallic or insulating.

Unlike weakly disordered metals, the resistivity of weakly pinned charge-density waves is not controlled by irrelevant momentum-relaxing processes. Instead, the leading contribution comes from incoherent diffusive processes that do not drag momentum and can be evaluated in the clean limit. We compute the DC resistivity analytically for a family of holographic charge-density-wave quantum-critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating, with possible relevance to underdoped cuprate high-temperature superconductors and strange metallic behavior.

Statistical systems near a classical critical point can be characterized through correlation functions, but computing physical quantities away from criticality requires information about the critical conformal theory. Recent progress in conformal-field-theory data, especially from the conformal bootstrap, motivates extending this information off criticality. We review and clarify how critical correlators can be used to calculate their behavior away from the critical point in a controlled way, requiring only scale invariance at criticality. The method is illustrated for different perturbations of the two-dimensional Ising model.

Precise scaling dimensions and OPE coefficients are now known for several three-dimensional universality classes through conformal bootstrap methods. We show how to use this information to obtain similarly precise estimates for off-critical correlators with conformal perturbation theory. We discuss spin-spin, energy-energy and spin-energy two-point functions in the high- and low-temperature regimes of the three-dimensional Ising model and evaluate leading and next-to-leading corrections. The spin-spin results agree with both Monte Carlo simulations and experimental estimates of the critical scattering function.

Magnetic field and momentum dissipation are key ingredients in condensed-matter systems. We incorporate them in gauge/gravity duality and systematically explore holographic infrared effective field theories based on Einstein-Maxwell-scalar models. The class of solutions studied appears insufficient to reproduce the phenomenology of charge transport in cuprates. In particular, we analyze the temperature scaling of the resistivity and Hall angle, highlighting both strengths and limitations of the approach.

Inspired by a conjectured universal bound for thermo-electric diffusion constants in quantum-critical strongly coupled systems, we investigate Planckian bounds in holographic models with momentum dissipation. For a simple massive-gravity dilaton model at zero charge density we find robust linear-in-temperature resistivity and entropy density alongside a constant electric susceptibility. We also find explicitly that the sum of the thermo-electric diffusion constants is bounded.

We provide an analytical derivation of thermo-electric transport coefficients in the simplest momentum-dissipating gauge/gravity model, where momentum non-conservation is realized by an explicit graviton mass in the bulk. We use a method developed for Q-lattices and models with momentum dissipation from non-trivial scalars. The analytical approach confirms results previously obtained numerically.

We present a systematic definition and analysis of thermo-electric linear response in gauge/gravity systems, focusing especially on massive-gravity models where the dual field theory dissipates momentum. A precise treatment of finite counterterms is essential for a consistent physical picture, whose hydrodynamic and beyond-hydrodynamic behavior matches field-theoretical expectations. The model provides a possible gauge/gravity description of a crossover from quantum-critical to disorder-dominated Fermi-liquid behavior, as expected in graphene.

We consider a free topological model in five-dimensional Euclidean flat spacetime built from two rank-two tensor fields. Although the bulk has no particular physical interpretation, non-trivial gauge field theories are recovered on its four-dimensional planar edge, with properties fixed by gauge and discrete symmetries. Time-reversal invariance is essential to obtain four-dimensional dynamics. One of the resulting edge models exhibits electromagnetic duality relating strong and weak coupling, and on shell coincides with Maxwell theory, which can therefore be viewed as a four-dimensional boundary theory of the five-dimensional topological model.

We study a generalization of the standard holographic p-wave superconductor with two interacting vector order parameters. Based on symmetry and linear response, we propose it as a holographic effective theory of a strongly coupled ferromagnetic superconductor. The two order parameters condense concomitantly, reflecting intertwined electric and magnetic dynamics. We characterize equilibrium and linear response, including optical conductivity and magnetic susceptibility, in the probe approximation and discuss backreaction in the normal phase by analogy with the unbalanced s-wave holographic superconductor.

We consider the fermionization of a bosonic free theory characterized by three-plus-one-dimensional scalar-tensor duality, interpreted as dimensional reduction through a planar boundary of five-dimensional topological BF theory. Using the Sommerfield tomographic representation of quantized bosonic fields, we explicitly construct a fermionic operator and Klein factor satisfying the correct anticommutation relations. The operator obeys the massless Dirac equation and can be identified with a three-plus-one-dimensional Weyl spinor. We also express the integrated charge density in terms of tomographically transformed bosonic degrees of freedom.

A planar boundary introduced in five-dimensional topological BF theory, subject only to locality and power counting, uniquely determines a gauge-invariant non-topological four-dimensional Lagrangian. The boundary condition on the bulk fields is interpreted as a duality relation for the boundary fields, analogous to fermionization duality in three dimensions. This suggests that the four-dimensional degrees of freedom might be fermionic despite originating from a bosonic bulk theory. The proposed dimensional-reduction method can be applied in generic spacetime dimension.

We consider four-dimensional Abelian topological BF theory with a planar boundary introduced following Symanzik's method. We find the most general boundary conditions compatible with the field equations broken by the boundary. Residual gauge invariance is described by two Ward identities that generate an algebra of conserved currents. We interpret this algebra as canonical commutation relations and use it to construct a three-dimensional Lagrangian. The unique boundary condition can also be read as a duality relation between three-dimensional dynamical variables.

We discuss two- and three-point correlators in the two-dimensional three-state Potts model in its high-temperature phase. Using form factors and perturbed conformal field theory we describe both large- and short-distance behavior, and compare with high-precision Monte Carlo simulations on the triangular lattice, finding agreement in both regimes. The results illuminate the three-quark correlator in the confining phase of (2+1)-dimensional SU(3) lattice gauge theory, suggesting a smooth crossover from a Delta-type law at short distances to a Y-type law at large distances.

The general form of the stress-tensor three-point function in four dimensions is obtained by solving Ward identities for diffeomorphism and Weyl symmetries. We discuss renormalization, scheme independence and analogies with the anomalous chiral triangle. At a critical point, the a and c coefficients of the four-dimensional trace anomaly are related to finite, scheme-independent amplitudes of the three-point function. Off criticality, the imaginary parts of these amplitudes satisfy sum rules expressing the total renormalization-group flow of a and c between critical points, although monotonicity of the flow remains unproven.

We study spin-spin, spin-energy and energy-energy correlators in the two-dimensional Ising model perturbed by a magnetic field. High-precision Monte Carlo simulations are compared with two approximations: a form-factor approach based on the exact S-matrix and a short-distance perturbative expansion around the conformal point. Both perform very well, with form factors more accurate beyond the correlation length and conformal perturbation more precise below it. We extend the perturbative analysis to second order in derivatives of the OPE constants to improve the agreement.

We propose an extension of the variational approach known as Truncated Conformal Space to compute numerically vacuum expectation values of operators in a conformal field theory perturbed by a relevant operator. As examples, we estimate the VEVs of ultraviolet-regular primary operators in the Ising and tricritical Ising conformal field theories under relevant perturbations and compare with independent predictions.

We apply an infrared-safe perturbative approach to compute short-distance corrections to scaling for correlators of primary operators in the critical two-dimensional Ising model in a magnetic field. Working with OPE Wilson coefficients rather than correlators yields all-order infrared-safe formulae and naturally produces the expected fractional powers of the magnetic field. Mellin transforms are used to control regularized integrals, and comparison with lattice data gives an estimate of the vacuum expectation value of the energy operator not fixed by standard non-perturbative approaches.

We consider renormalizable theories without relevant couplings and present an infrared-consistent technique to study corrections to short-distance behavior, expressed through Wilson OPE coefficients, due to a relevant perturbation. The method reformulates earlier work with a more orthodox treatment of ultraviolet divergences, leading to simpler formulae and an explicit all-order, regularization-invariant proof of infrared finiteness. The underlying hypotheses are discussed and shown to hold in conformal theories, which provide a natural domain of application.

We present a QCD analysis of recently published data on jet production in Z0 decays. At the Z0 energy one can also analyze jet-shape variables that were disregarded at lower-energy electron-positron experiments because of their large hadronization sensitivity. We discuss the possibility of extracting from jet data detailed features of the colour structure of radiative corrections to three-jet production.

Target-space duality is incorporated in previously proposed effective actions describing non-perturbative supersymmetry breaking in string theory via gaugino condensation. Duality-preserving vacua with broken supersymmetry and fixed unified coupling constant occur generically. The question of the vanishing of the cosmological constant is also briefly addressed.

We study the gravitino condensate in the one-loop approximation around a non-trivial background metric. Among known regular solutions of the Euclidean Einstein equations, the Eguchi-Hanson metric is the unique relevant configuration. Standard functional integration gives a finite gravitino condensate. Because of an anomalous supersymmetry transformation law, this implies that local supersymmetry is spontaneously broken in supergravity models with scalar multiplets.