Symmetries and operators in $T\bar{T}$ deformed CFTs (2507.08588v1)

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) {\it {dressed}} operators, which are primary operators with respect to the nonlocal conformal symmetries, and (ii) {\it 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. %Crucially, while maintaining locality, these physical operators enable the use of conformal symmetry to systematically compute physical quantities such as correlation functions. We calculate the two-point correlation functions of these operators in momentum space and find that our results align with both string theory predictions \cite{Cui:2023jrb} and field theory calculations \cite{Aharony:2023dod}. Additionally, we explore the relationship between physical operators and alternative operator definitions proposed in the literature.