Topological Gauging and Double Current Deformations

TL;DR

This paper develops a quantum framework for solvable deformations of 2D quantum field theories driven by conserved currents, revealing connections to T-duality, TsT transformations, and Yang-Baxter deformations, with exact S-matrix dressing.

Contribution

It introduces a path integral-based formalism for topological gauging deformations, extending to non-Abelian currents and linking to known integrable models and algebraic structures.

Findings

Deformation preserves conformality in certain free boson theories.

Deformation corresponds to TsT transformations in specific cases.

Connection established between T Tbar deformation and central extensions of symmetry algebras.

Abstract

We study solvable deformations of two-dimensional quantum field theories driven by a bilinear operator constructed from a pair of conserved $U(1)$ currents $J^a$. We propose a quantum formulation of these deformations, based on the gauging of the corresponding symmetries in a path integral. This formalism leads to an exact dressing of the $S$-matrix of the system, similarly as what happens in the case of a $\mathrm{T}\overline{\mathrm{T}}$ deformation. For conformal theories the deformations under study are expected to be exactly marginal. Still, a peculiar situation might arise when the conserved currents $J^a$ are not well-defined local operators in the original theory. A simple example of this kind of system is provided by rotation currents in a theory of multiple free, massless, non-compact bosons. We verify that, somewhat unexpectedly, such a theory is indeed still conformal after deformation and that it coincides with a TsT transformation of the original system. We then extend our formalism to the case in which the conserved currents are non-Abelian and point out its connection with Deformed T-dual Models and homogeneous Yang-Baxter deformations. In this case as well the deformation is based on a gauging of the symmetries involved and it turns out to be non-trivial only if the symmetry group admits a non-trivial central extension. Finally we apply what we learned by relating the $\mathrm{T}\overline{\mathrm{T}}$ deformation to the central extension of the two-dimensional Poincar\'{e} algebra.