Locality and Conserved Charges in $T\overline{T}$-Deformed CFTs

TL;DR

This paper explores the locality and conserved charges in $T\overline{T}$-deformed conformal field theories, providing a Hamiltonian that reproduces the spectrum and analyzing the locality of KdV charges.

Contribution

It constructs a Hamiltonian up to third order in deformation that reproduces the spectrum and discusses the locality of conserved charges in $T\overline{T}$-deformed CFTs.

Findings

Hamiltonian reproduces the Zamolodchikov spectrum

Hamiltonian includes new central charge terms

KdV charges can be made local to first order

Abstract

We investigate the locality properties of $T \overline T$-deformed CFTs within perturbation theory. Up to third order in the deformation parameter, we find a Hamiltonian operator which solves the flow equation, reproduces the Zamolodchikov energy spectrum, and is consistent with quasi-locality of the theory. This Hamiltonian includes terms proportional to the central charge which have not appeared before and which are necessary to reproduce the correct spectrum. We show that the Hamiltonian is not uniquely defined since it contains free parameters, starting at second order, which do not spoil the above properties. We then use it to determine the full conserved stress tensor. In our approach, the KdV charges are automatically conserved to all orders but are not a priori local. Nevertheless, we show that they can be made local to first order. Our techniques allow us to further comment on the space of Hamiltonians constructed from products of KdV charges which also flow to local charges in the deformed theory in the IR.