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

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.

💡 Research Summary

The paper addresses the description of D‑branes and Ramond–Ramond (RR) fields on global orbifolds (X/G) of Type II string theory in the absence of NS‑NS three‑form flux. While ordinary (equivariant) K‑theory (K_{G}^{\bullet}(X)) correctly classifies topological RR charges, it fails to capture the full structure of twisted sectors that appear in orbifold conformal field theory. The authors propose to replace the usual group cohomology with Bredon equivariant cohomology, a theory that records, for each group element (g\in G), the ordinary cohomology of the fixed‑point set (X^{g}). This “stringy” cohomology coincides with Chen–Ruan orbifold cohomology and therefore provides the appropriate mathematical language for orbifold backgrounds.

A central technical achievement is the construction of an equivariant Chern character \