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 Ja. 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 \( \textrm{T}\overline{\textrm{T}} \) deformation. For conformal theories the deformations under study are expected to be exactly marginal. Still, a peculiar situation might arise when the conserved currents Ja 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 \( \textrm{T}\overline{\textrm{T}} \) deformation to the central extension of the two-dimensional Poincaré algebra.
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Acknowledgments
We thank Ofer Aharony, Victor Gorbenko, and Yifan Wang for fruitful discussions. This work is supported in part by the NSF grant PHY-2210349, by the BSF grant 2018068 and by the Simons Collaboration on Confinement and QCD Strings. S.N. wishes to thank the Department of Physics of the Università degli Studi di Torino for its kind hospitality
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Dubovsky, S., Negro, S. & Porrati, M. Topological gauging and double current deformations. J. High Energ. Phys. 2023, 240 (2023). https://doi.org/10.1007/JHEP05(2023)240
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DOI: https://doi.org/10.1007/JHEP05(2023)240