Defects, Super-Poincar\'{e} line bundle and Fermionic T-duality

TL;DR

This paper explores topological defects in conformal field theories, focusing on how bosonic and fermionic T-dualities are encoded through the Super-Poincaré line bundle and their relation to Fourier-Mukai transforms of Ramond-Ramond fields.

Contribution

It generalizes the understanding of topological defects to include fermionic T-duality and introduces the Super-Poincaré line bundle as a key structure in this context.

Findings

Bosonic T-duality is encoded by defect equations of motion.

Fermionic T-duality is implemented via the Super-Poincaré line bundle.

The Fourier-Mukai transform kernel extends to fermionic T-duality via supermanifold integration.

Abstract

Topological defects are interfaces joining two conformal field theories, for which the energy momentum tensor is continuous across the interface. A class of the topological defects is provided by the interfaces separating two bulk systems each described by its own Lagrangian, where the two descriptions are related by a discrete symmetry. In this paper we elaborate on the cases in which the discrete symmetry is a bosonic or a fermionic T- duality. We review how the equations of motion imposed by the defect encode the general bosonic T- duality transformations for toroidal compactifications. We generalize this analysis in some detail to the case of topological defects allowed in coset CFTs, in particular to those cosets where the gauged group is either an axial or vector U(1). This is discussed in both the operator and Lagrangian approaches. We proceed to construct a defect encoding a fermionic T-duality. We show that the fermionic T-duality is implemented by the Super-Poincar\'{e} line bundle. The observation that the exponent of the gauge invariant flux on a defect is a kernel of the Fourier-Mukai transform of the Ramond-Ramond fields, is generalized to a fermionic T-duality. This is done via a fiberwise integration on supermanifolds.