Schwarzian for colored Jackiw-Teitelboim gravity

TL;DR

This paper derives a generalized Schwarzian boundary action for colored JT gravity from an $su(N,N)$ BF formulation, analyzing its properties, stability, and implications for quantum chaos in rainbow-AdS$_2$ geometries.

Contribution

It introduces the color generalization of the Schwarzian action for colored JT gravity derived from an $su(N,N)$ BF formulation, including analysis of stability and quantum chaos.

Findings

Derived the boundary action as a color generalization of Schwarzian.

Analyzed stability and instability of spin-1 modes.

Discussed implications for quantum chaos in rainbow-AdS$_2$ geometries.

Abstract

We study the boundary effective action of the colored version of the Jackiw-Teitelboim (JT) gravity. We derive the boundary action, which is the color generalization of the Schwarzian action, from the $su(N,N)$ BF formulation of the colored JT gravity. Using different types of the $SU(N,N)$ group decompositions both the zero and finite temperature cases are elaborated. We provide the semi-classical perturbative analysis of the boundary action and discuss the instability of the spin-1 mode and its implication for the quantum chaos. A rainbow-AdS$_2$ geometry is introduced where the color gauge symmetry is spontaneously broken.