Characters of irrelevant deformations

Shouvik Datta,Yunfeng Jiang

doi:10.1007/jhep07(2021)162

Shouvik Datta, Yunfeng Jiang

Open Access

https://doi.org/10.1007/jhep07(2021)162

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Abstract

We analyse the Toverline{T} deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve Toverline{T} , Joverline{T} and Toverline{J} simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

Highlights

JHEP07(2021)162 exactly solvable, this question can be readily addressed provided we express the quantity as a sum over Boltzmann factors
We evaluate the quantity using three methods, which establishes the consistency our results; the methods being: (i) using the explicit form of the deformed spectrum [3, 4] and performing the 1/c expansion; (ii) writing the deformed partition function as an integral transformation of the undeformed one [14, 15] and performing a saddle-point analysis in the large c limit; and (iii) performing an 1/c expansion for the flow equation of the torus partition function [16,17,18]
We studied a double-scaling limit of T Tdeformed characters in the 1/c expansion

Summary

Introduction

JHEP07(2021)162 exactly solvable, this question can be readily addressed provided we express the quantity as a sum over Boltzmann factors. Following the analysis for the pure T Tdeformation, we obtain the O(c) and O(c0) contributions to deformed characters. When restricting to the pure gravity sector and one specific sign of the deformation parameter, it is equivalent at large c to putting a cutoff surface in AdS [10,11,12]. This latter interpretation is rather intuitive and triggered a lot of activities at the early stages of the development..

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