Cluster decomposition, T-duality, and gerby CFTs

Abstract

In this paper, we study conformal field theories (CFTs) associated to gerbes. These theories suffer from a lack of cluster decomposition, but this problem can be resolved: the CFTs are the same as CFTs for disconnected targets. Such theories also lack cluster decomposition, but in that form, the lack is manifestly not very problematic. In particular, we shall see that this matching of CFTs, this duality between noneffective-gaugings and sigma models on disconnected targets, is a worldsheet duality related to T-duality. We perform a wide variety of tests of this claim, ranging from checking partition functions at arbitrary genus to D-branes to mirror symmetry. We also discuss a number of applications of these results, including predictions for quantum cohomology and Gromov-Witten theory and additional physical understanding of the geometric Langlands program.