Geometric realization via irrelevant deformations induced by the stress-energy tensor

TL;DR

This paper develops a formalism for stress-energy tensor driven deformations of quantum field theories, providing exact solutions and exploring their connections to gravitational models and scalar field theories.

Contribution

It introduces a general approach relating stress-energy tensor deformations to metric flow equations in arbitrary dimensions, including exact solutions for specific deformations.

Findings

Exact solutions for $T\bar{T}$ and polynomial stress tensor deformations.

Perturbative methods reproduce the exact solutions.

Applications to gravitational models and scalar field theories.

Abstract

In this paper, we generalize the deformations driven by the stress-energy tensor $T$ and investigate their relation to the flow equation for the background metric at the classical level. For a deformation operator $\mathcal{O}$ as a polynomial function of the stress-energy tensor, we develop a formalism that relates a deformed action to a flow equation for the metric in arbitrary spacetime dimensions. It is shown that in the $T\bar{T}$ deformation and the $\mathcal{O}(T)=\text{tr}[\textbf{T}]^m$ deformation, the flow equations for the metric allow us to directly obtain exact solutions in closed forms. We also demonstrate the perturbative approach to find the same results. As several applications of the $\mathcal{O}(T)=\text{tr}[\textbf{T}]^m$ deformation, we discuss the relation between the deformations and gravitational models. Besides, we also deform the Lagrangians for scalar field theories.