Flows in the Space of Interacting Chiral Boson Theories

We study interacting theories of N left-moving and N̄ right-moving Floreanini-Jackiw bosons in two dimensions. A parameterized family of such theories is shown to enjoy (non-manifest) Lorentz invariance if and only if its Lagrangian obeys a flow equation driven by a function of the energy-momentum tensor. We discuss the canonical quantization of such theories along classical stress tensor flows, focusing on the case of the root-T T̄ deformation, where we obtain perturbative results for the deformed spectrum in a certain large-momentum limit. In the special case N = N̄, we consider the quantum effective action for the root-T T̄-deformed theory by expanding around a general classical background, and we find that the one-loop contribution vanishes for backgrounds with constant scalar gradients. Our analysis can also be interpreted via dual $U(1)$ Chern-Simons theories in three dimensions, which might be used to describe deformations of charged AdS₃ black holes or quantum Hall systems.