A general definition of $J{T}_a$ -- deformed QFTs

Abstract

We propose a general path-integral definition of two-dimensional quantum field theories deformed by an integrable, irrelevant vector operator constructed from the components of the stress tensor and those of a $U(1)$ current. The deformed theory is obtained by coupling the original QFT to a flat dynamical gauge field and "half" a flat dynamical vielbein. The resulting partition function is shown to satisfy a geometric flow equation, which perfectly reproduces the flow equations for the deformed energy levels that were previously derived in the literature. The S-matrix of the deformed QFT differs from the original S-matrix only by an overall phase factor that depends on the charges and momenta of the external particles, thus supporting the conjecture that such QFTs are UV complete, although intrinsically non-local. For the special case of an integrable QFT, we check that this phase factor precisely reproduces the change in the finite-size spectrum via the Thermodynamic Bethe Ansatz equations.

21 pages, v2 signs fixed

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• Topological Gauging and Double Current Deformations
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• $T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS${}_3$ gravity with mixed boundary conditions
• States, symmetries and correlators of $T\bar{T}$ and $J\bar{T}$ symmetric orbifolds
• Irrelevant Deformations with Boundaries and Defects
• Irrelevant and marginal deformed BMS field theories
• Characters of irrelevant deformations
• String Duals of Two-Dimensional Yang-Mills and Symmetric Product Orbifolds