2013/01/30 by Alexander Kahle, Kahle, Alexander, Ruben Minasian +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematics and Applications #hep-th #math.DG
paper · pdf · doi:10.48550/arxiv.1301.7238
arxiv created 2013/01/30 · openalex publication_date 2013/01/30 · arxiv updated 2013/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is to re-examine D-brane Ramond-Ramond field couplings in the presence of a B-field. We will argue that the generalised geometry induced on the world volume by the B-field results in an important but subtle change on the coupling. In order to explain this, we use the language of differential K-theory. The expression determining the coupling is then seen to be a consequence of the Riemann-Roch theorem. Our key assertion is that the appropriate Riemann-Roch theorem changes in the presence of the B-field. In particular, the A-hat forms appearing in the theorem are now constructed using the torsionful Levi-Civita connection associated to the generalised geometry. As we shall see, the resulting expression not only agrees with recently discovered local couplings on the D-brane worldvolume involving RR fields and derivatives of the B-field, but also makes the coupling manifestly T-duality invariant.