Twisted K-Theory as a BRST Cohomology

Abstract

We use the BRST formalism to classify the gauge orbits of type II string theory's Ramond-Ramond (RR) field strengths under large RR gauge transformations of the RR gauge potentials. We find that this construction is identical to the Atiyah-Hirzebruch spectral sequence construction of twisted K-theory, where the Atiyah-Hirzebruch differentials are the BRST operators. The actions of the large gauge transformations on the field strengths that lie in an integral lattice of de Rham cohomology are found using supergravity, while the action on Z_2 torsion classes is found using the Freed-Witten anomaly. We speculate that an S-duality covariant classification may be obtained by including NSNS gauge transformations and using the BV formalism. An example of a Z_3 torsion generalization of the Freed-Witten anomaly is provided.