Renormalization of Lorentz non-invariant actions and manifest T-duality

TL;DR

This paper investigates non-Lorentz invariant two-dimensional sigma-models, demonstrating how emergent Lorentz symmetry constrains their structure, and shows that their quantum properties align with T-duality invariance, ensuring consistent renormalization.

Contribution

It introduces a class of sigma-models with group-theoretic structures that recover Lorentz invariance on-shell and analyzes their one-loop renormalization, linking quantum behavior to classical T-duality.

Findings

Quantum Lorentz anomaly is absent in these models.

The running of couplings matches that of T-dual models.

Constraints commute with quantization in studied examples.

Abstract

We study general two-dimensional sigma-models which do not possess manifest Lorentz invariance. We show how demanding that Lorentz invariance is recovered as an emergent on-shell symmetry constrains these sigma-models. The resulting actions have an underlying group-theoretic structure and resemble Poisson-Lie T-duality invariant actions. We consider the one-loop renormalization of these models and show that the quantum Lorentz anomaly is absent. We calculate the running of the couplings in general and show, with certain non-trivial examples, that this agrees with that of the T-dual models obtained classically from the duality invariant action. Hence, in these cases solving constraints before and after quantization are commuting operations.