Cluster decomposition, T-duality, and gerby CFT's

TL;DR

This paper explores the duality between gerby conformal field theories and sigma models on disconnected targets, revealing a T-duality connection and providing insights into quantum cohomology, Gromov-Witten theory, and the geometric Langlands program.

Contribution

It demonstrates that gerby CFTs are equivalent to CFTs on disconnected targets, resolving cluster decomposition issues and establishing a worldsheet T-duality.

Findings

Matching of gerby CFTs with disconnected target CFTs

Partition functions and D-branes support the duality

Applications to quantum cohomology and geometric Langlands

Abstract

In this paper we study CFT's associated to gerbes. These theories suffer from a lack of cluster decomposition, but this problem can be resolved: the CFT's are the same as CFT's 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 CFT's, 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.