Nonperturbative aspects of two-dimensional $T\bar{T}$-deformed scalar theory from functional renormalization group

TL;DR

This paper investigates the nonperturbative properties of two-dimensional $T\bar{T}$-deformed scalar field theory using the functional renormalization group, revealing a nontrivial fixed point and suggesting nonperturbative renormalizability.

Contribution

It derives the beta functions and identifies a nontrivial fixed point in $T\bar{T}$-deformed scalar theory, indicating a new universality class and potential nonperturbative renormalizability.

Findings

Identification of a nontrivial fixed point

Relevance of the deformation parameter at the fixed point

Potential nonperturbative renormalizability of the theory

Abstract

We study $T\bar{T}$-deformed $O(N)$ scalar field theory in two-dimensional spacetime using the functional renormalization group. We derive the $\beta$ functions for the couplings in the system and explore the fixed points. In addition to the Gaussian (trivial) fixed point, we find a nontrivial fixed point at which a new universality class exists. The deformation parameter becomes relevant at the nontrivial fixed point. Therefore, the $T\bar T$-deformed scalar field theory in two-dimensional spacetime could be defined as a nonperturbatively renormalizable theory.