Quantum structure of T-dualized models with symmetry breaking

TL;DR

This paper investigates the T-duality of principal sigma-models with symmetry breaking, deriving conditions for torsionlessness and one-loop renormalizability, and applies these to Bianchi models to analyze their quantum properties.

Contribution

It provides explicit formulas for the torsion and Ricci tensor of dual models with symmetry breaking and proves inheritance of renormalizability, extending understanding of T-duality in broken symmetry contexts.

Findings

Dual models inherit one-loop renormalizability from original models.

Conditions for dual models to be torsionless are established.

Certain Bianchi models exhibit absence of dilaton anomaly under specific parameters.

Abstract

We study the principal sigma-models defined on any group manifold GL x GR/GD with breaking of GR, and their T-dual transforms. For abritary breaking we can express the torsion and Ricci tensor of the dual model in terms of the frame geometry of the initial principal model. Using these results, we give necessary and sufficient conditions for the dual model to be torsionless and prove that the one-loop renormalizability of a given principal model is inherited by its dual partner, who shares the same beta-functions. These results are shown to hold also if the principal model is endowed with torsion. As an application we compute the beta-functions for the full Bianchi family and show that for some choices of the breaking parameters the dilaton anomaly is absent: for these choices the dual torsion vanishes. For the dualized Bianchi V model (which is torsionless for any breaking), we take advantage of its simpler structure, to study its two-loops renormalizability.