Aspects of Quantum Fermionic T-duality

TL;DR

This paper investigates fermionic T-duality in sigma models, addressing potential obstructions and extending the duality beyond classical levels, with implications for quantum conformal invariance.

Contribution

It provides a detailed analysis of fermionic T-duality in supergroup coset models, deriving dual models and verifying their quantum conformal invariance.

Findings

Derived fermionic T-duals using non-abelian T-duality and gauge fixing.

Proved conformal invariance at one and two loops for these models.

Validated Ward Identities confirming quantum consistency.

Abstract

We study two aspects of fermionic T-duality: the duality in purely fermionic sigma models exploring the possible obstructions and the extension of the T-duality beyond classical approximation. We consider fermionic sigma models as coset models of supergroups divided by their maximally bosonic subgroup OSp(m|n)/SO(m) x Sp(n). Using the non-abelian T-duality and a non-conventional gauge fixing we derive their fermionic T-duals. In the second part of the paper, we prove the conformal invariance of these models at one and two loops using the Background Field Method and we check the Ward Identities.