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.
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Communicated by N.A. Nekrasov
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Szabo, R.J., Valentino, A. Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory. Commun. Math. Phys. 294, 647–702 (2010). https://doi.org/10.1007/s00220-009-0975-1
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DOI: https://doi.org/10.1007/s00220-009-0975-1