Defining Root-$T\overline{T}$ operator

TL;DR

This paper proposes a tentative definition of the Root-$T\overline{T}$ operator in 2D quantum conformal field theories, exploring its properties through correlation function variations.

Contribution

It introduces a novel definition of the Root-$T\overline{T}$ operator in generic 2D CFTs, expanding understanding of such operators beyond specific models.

Findings

Explicit computation of correlation function variations

Investigation of operator properties

Proposed factorization assumptions

Abstract

We give a tentative definition of the recently introduced Root-$T\bar{T}$ operator in a generic, two dimensional quantum conformal field theory with continuous spectrum of scaling weights. The definition assumes certain factorization properties and uses Schwinger parametrization to introduce the square root. Properties of the operator thus defined are investigated by explicit computation of variations of two- and three-point correlation functions.