Defects, Non-abelian T-duality, and the Fourier-Mukai transform of the Ramond-Ramond fields

TL;DR

This work extends the Fourier-Mukai framework for Ramond-Ramond field transformations to non-abelian T-duality by constructing topological defects that implement duality for isometry groups acting without isotropy. The authors derive a non-abelian RR-transform formula ${\widehat{{\cal G}}=\int_G {\cal G}\wedge e^{\hat{B}-B-dx^a\wedge L^a-{1\over 2}x^a f_{bc}^a L^b\wedge L^c}}$ from the defect flux, and demonstrate that the defect equations of motion reproduce the non-abelian duality relations. The paper provides an explicit SU(2) example, showing how the dual RR fields can be computed in a compact form and checked against known results, while preserving Bianchi identities. It also outlines future directions toward K-theory elevation, generalization to other groups, and extensions to isotropy-acted dualities, highlighting the broad relevance for D-brane charge transformations under non-abelian dualities.

Abstract

We construct topological defects generating non-abelian T-duality for isometry groups acting without isotropy. We find that these defects are given by line bundles on the correspondence space with curvature which can be considered as a non-abelian generalization of the curvature of the Poincarè bundle. We show that the defect equations of motion encode the non-abelian T-duality transformation. The Fourier-Mukai transform of the Ramond-Ramond fields generated by the gauge invariant flux of these defects is studied. We show that it provides elegant and compact way of computation of the transformation of the Ramond-Ramond fields under the non-abelian T-duality.