Exact $T\overline{T}$ deformation of two-dimensional Maxwell theory

TL;DR

This paper analyzes the exact nonperturbative effects of $Tar{T}$ deformation on 2D Maxwell theory, revealing spectrum truncation, nonperturbative modifications, and phase transitions depending on the deformation parameter.

Contribution

It provides an exact expression for the deformed partition function including nonperturbative effects, and explores the resulting spectral and phase structure of the theory.

Findings

Spectrum truncation for positive deformation parameter

Nonperturbative regularization of divergences for negative parameter

Infinite-order phase transitions linked to Polyakov-loop behavior

Abstract

$T\overline{T}$-deformed two-dimensional quantum Maxwell theory on the torus is examined, taking into account nonperturbative effects in the deformation parameter $\mu$. We study the deformed partition function solving the relevant flow equation at the level of individual flux sectors. Summing exactly the "instanton" series, we obtain a well-defined expression for the partition function at arbitrary $\mu$. For $\mu>0$, the quantum spectrum of the theory experiences a truncation, the partition function reducing to a sum over a finite set of positive-energy states. For $\mu<0$ instead, the appearance of nonperturbative contributions in $\mu$ drastically modifies the structure of the partition function, regularizing its naive divergences through instanton-like subtractions. For each flux sector, we show that the semiclassical contribution is dominated by the deformed classical action. The theory is observed to undergo infinite-order phase transitions for certain values of $\mu$, associated with the vanishing of Polyakov-loop correlators.