Root-$T \overline{T}$ Deformations in Two-Dimensional Quantum Field Theories

Abstract: In this letter we introduce a one-parameter deformation of two-dimensional quantum field theories generated by a non-analytic operator which we call Root-$T \overline{T}$. For a conformal field theory, the operator coincides with the square-root of the $T \overline{T}$ operator. More generally, the operator is defined so that classically it is marginal and generates a flow which commutes with the $T \overline{T}$-flow. Intriguingly, the Root-$T \overline{T}$ flow is closely related to the ModMax theory recently constructed by Bandos, Lechner, Sorokin and Townsend.