Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory

TL;DR

This paper explores the mathematical structure of D-branes and Ramond-Ramond fields on orbifolds using equivariant K-theory, revealing new consistency conditions and couplings relevant for string theory.

Contribution

It introduces a novel framework combining equivariant K-theory and Bredon cohomology to analyze Ramond-Ramond fields and D-branes on orbifolds, including new couplings and quantization rules.

Findings

Bredon cohomology captures orbifold stringy features.

New Ramond-Ramond couplings are defined via equivariant K-theory.

A Dirac quantization rule for fluxes is derived.

Abstract

We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the low-energy effective field theory, and which provides new consistency conditions for fractional D-branes and Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings of D-branes which generalize previous examples. We propose a definition for groups of differential characters associated to equivariant K-theory. We derive a Dirac quantization rule for Ramond-Ramond fluxes, and study flat Ramond-Ramond potentials on orbifolds.