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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
Ebert et al. (Mon,) studied this question.