Symmetries and operators in $T\bar{T}$ deformed CFTs

TL;DR

This paper constructs and analyzes two classes of operators in $T\bar{T}$-deformed conformal field theories, revealing their properties and correlations, and compares them with string theory and existing literature.

Contribution

It introduces a new class of local physical operators and explicitly constructs dressed operators, clarifying their roles in the nonlocal symmetry structure of $T\bar{T}$-deformed CFTs.

Findings

Two-point functions match string theory predictions.

Dressed operators are nonlocal but preserve conformal symmetry.

Physical operators are local and related to dressed operators.

Abstract

$T\bar{T}$-deformed CFTs are known to possess nonlocal conformal symmetries that do not act tractably on the undeformed local operators. In this paper, we explicitly construct two distinct classes of operators: (i) dressed operators, which are primary operators with respect to the nonlocal conformal symmetries, and (ii) physical operators, a new type of local operator we introduce. While the dressed operators preserve the conformal symmetry structure, they are themselves nonlocal. The physical operators, by contrast, are local and can be expressed in terms of the dressed operators. We calculate the two-point correlation functions of these operators in momentum space and find that our results align with both string theory predictions and field theory calculations. Additionally, we explore the relationship between physical operators and alternative operator definitions proposed in the literature.