Butterflies in $\textrm{T}\overline{\textrm{T}}$ deformed anomalous CFT$_2$

TL;DR

This paper investigates quantum chaos in $ extrm{T}ar{ extrm{T}}$-deformed 2D CFTs with anomalies, analyzing chaos indicators and holographic duals, revealing bound saturation and complex chaotic responses in certain regimes.

Contribution

It provides a detailed analysis of chaos in deformed CFTs with anomalies, including holographic dual descriptions and the impact of deformation on chaos parameters.

Findings

Chaos bound remains saturated despite deformation.

Butterfly velocity depends nontrivially on deformation and anomaly.

A Hagedorn regime causes chaotic response to become complex.

Abstract

We study quantum chaos in $\textrm{T}\overline{\textrm{T}}$-deformed two-dimensional conformal field theories with gravitational anomaly and their holographic dual description in topologically massive gravity. Using pole-skipping and shock-wave analysis, we extract the Lyapunov exponent and butterfly velocity and analyze the interplay between irrelevant deformation and parity-violating dynamics. We find that the chaos bound remains saturated, while the butterfly velocity exhibits nontrivial dependence on the deformation parameter and anomaly. We also identify a Hagedorn regime in which the chaotic response becomes complex valued, signaling a breakdown of the physical branch of the deformed theory.