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

Abstract

We study quantum chaos in $\text{T}\overline{\text{T}}$-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.

42 pages, 4 figures and 2 appendices