Pole-skipping without master variable and holographic superfluids

TL;DR

This work removes the master-variable restriction in pole-skipping analysis by formulating a matrix-based approach for multi-field holographic systems and applies it to holographic superfluids. It demonstrates that not all hydrodynamic poles (e.g., diffusion) are pole-skipping and that, even near a superconducting transition, a massless order parameter does not generate new pole-skipping points. The paper provides both horizon-Frobenius-based computations and boundary-quantity (μ,ε) expressions for pole-skipping points, including near-critical expansions. A formal argument shows pole-skipping at w = −in arises in multi-field systems under mild assumptions, illustrating how to systematically identify pole-skipping points without a master variable.

Abstract

The pole-skipping is a universal property of Green's functions at strong coupling found by the AdS/CFT duality. There is a conventional formalism of the pole-skipping, but it relies on the existence of a "master variable." Namely, it is applicable to a system with a single field. We propose an alternative formalism that does not rely on a master variable. As an example, we study the pole-skipping of holographic superfluids. A "hydrodynamic" pole such as the diffusion pole is usually regarded as a pole-skipping point. But we point out that not all hydrodynamic poles are pole-skipping points.