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

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.

arXiv comment6 pages, 2 figures

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• Sequential Flows by Irrelevant Operators
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• String Duals of Two-Dimensional Yang-Mills and Symmetric Product Orbifolds