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 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.