Composite operators in $T\bar T$-deformed free QFTs

TL;DR

This paper investigates how composite operators, especially the stress-energy tensor, are renormalized in $T\bar T$-deformed free quantum field theories, revealing different behaviors in massive and massless cases.

Contribution

It provides a detailed perturbative analysis of operator renormalization in $T\bar T$-deformed free QFTs, highlighting differences between massive and massless theories.

Findings

Massless case: stress tensor not renormalized up to high order.

Massive case: linear order counterterms are induced.

Results agree with recent general formulas for the massless case.

Abstract

We study perturbative renormalization of the composite operators in the $T\bar T$-deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases. While in the latter case the canonical stress tensor is not renormalized up to high order in the perturbative expansion, in the massive theory there are induced counterterms at linear order. For a massless theory our results match the general formula derived recently in [1].