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

Understand

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.