Abstract
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-Poincaré 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.
Highlights
Inserting a defect/interface in the path integral is equivalent in the operator language to the insertion of an operator D which maps the Hilbert space of CFT 1 to that of CFT 2
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
A topological defect can be moved to the boundary and fused with it, producing new boundary conditions [3, 8, 11]
Summary
We review some basic facts concerning topological defects and their relation to T-duality. In the subsection we generalize this to the factorized T-duality in non-linear sigma models with isometries. In these cases the null space of the defects is trivial and the defects are invertible. We review defects implementing generators of the full O(d, d|Z) duality group in the case of toroidal compactification. We conclude this section explaining how the T-duality transformation of the Ramond-Ramond charges can be written as the Fourier-Mukai transform with the kernel given by the exponent of the gauge invariant flux on the corresponding topological defect
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