Flows in the space of interacting chiral boson theories

Abstract

We study interacting theories of N left-moving and N¯ right-moving Floreanini-Jackiw bosons in two dimensions. A parametrized family of such theories is shown to enjoy (nonmanifest) 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-TT¯ deformation, where we obtain perturbative results for the deformed spectrum in a certain large-momentum limit. In the special case N=N¯, we consider the quantum effective action for the root-TT¯-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. Published by the American Physical Society 2024