In the last few years, much attention has been devoted to the study of a peculiar class of irrelevant deformations of 2-dimensional Quantum Field Theories, known as “Solvable Irrelevant Deformations”. The poster child of these is the celebrated “TTbar deformation”. They display unusual properties in the UV, which can be described exactly, their irrelevant nature notwithstanding. For this reason they represent a sensible extension of Quantum Field Theory beyond the Wilsonian paradigm and have attracted a considerable attention from the high energy theory community. The property of being solvable is shared with a wider class of deformations, constructed out of pairs of conserved currents. In general these are marginal deformations, thus presenting very different UV properties. Nonetheless their structures are similar to the TTbar ones, hinting at the existence of a universal description.
In this talk I will present a very general framework that accommodates both solvable irrelevant and solvable marginal deformations, which amounts to a “topological gauging” of the symmetries of the system. Through simple path integral computations, I will recover the main features of these theories and show their equivalence to TST and Yang-Baxter deformations. For the case of TTbar, the topological gauging perspective explains the previously not understood relation to field theory in non-commutative Minkowski space-time and to the centrally extended Poincaré algebra.