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

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.

46 pages; v2: typos corrected

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Cited by in corpus (12)

• 8d gauge anomalies and the topological Green-Schwarz mechanism
• Differential K-theory. A survey
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Differential orbifold K-Theory
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Differential Equivariant K-Theory
• Flux Quantization on M5-branes
• Anyons on M5-Probes of Seifert 3-Orbifolds via Flux Quantization
• Proper Orbifold Cohomology
• Differential cohomology (encyclopedia article)
• Twisted differential K-characters and D-branes
• Stratified Fiber Bundles, Quinn Homology and Brane Stability of Hyperbolic Orbifolds