Topological gauging and double current deformations

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