Weyl corrections to diffusion and chaos in holography

TL;DR

This paper explores how Weyl corrections influence thermal diffusion and quantum chaos in holographic models, revealing non-universal modifications to established bounds and relations at IR fixed points.

Contribution

It introduces Weyl coupling into the EMDA holographic framework and analyzes its impact on thermal diffusion and chaos, highlighting non-universal corrections.

Findings

Weyl coupling modifies thermal diffusion constant and butterfly velocity differently.

The ratio D_Q/(v_B^2 τ_L) acquires non-universal Weyl-dependent corrections.

The universal bound relating diffusion and chaos is altered by matter field effects.

Abstract

Using holographic methods in the Einstein-Maxwell-dilaton-axion (EMDA) theory, it was conjectured that the thermal diffusion in a strongly coupled metal without quasi-particles saturates an universal lower bound that is associated with the chaotic property of the system at infrared (IR) fixed points~\cite{blake:1705}. In this paper, we investigate the thermal transport and quantum chaos in the EMDA theory with a small Weyl coupling term. It is found that the Weyl coupling correct the thermal diffusion constant $D_Q$ and butterfly velocity $v_B$ in different ways, hence resulting a modified relation between the two at IR fixed points. Unlike that in the EMDA case, our results show that the ratio $D_Q/ (v_B^2\tau_L)$ always contains a {\it non-universal} Weyl correction which depends on the matter fields as long as the $U(1)$ current is relevant in the IR.