Modular transformations of on-shell actions of (root-)$\text{T}\overline{\text{T}}$ deformed holographic CFTs

TL;DR

This paper investigates how modular transformations affect the on-shell actions of gravity solutions dual to (root-)$\text{T}\overline{\text{T}}$ deformed holographic CFTs, revealing insights into their holographic structure.

Contribution

It provides a holographic analysis of the modular properties of (root-)$\text{T}\overline{\text{T}}$ deformed CFTs by computing on-shell actions of gravity saddle points.

Findings

Modular transformations relate different gravity saddle solutions.

The study reveals the structure of deformed CFT partition functions under modular transformations.

Insights into gravitational duals of deformed CFTs are obtained.

Abstract

In this study, we examine the modular transformations of the (root-)$\text{T}\overline{\text{T}}$ deformed torus partition function of a two-dimensional CFT (with a gravitational anomaly) from the holographic perspective by computing the on-shell actions of various saddle solutions of the dual gravity theories.