2019/10/30 by Julius Eckhard, Heeyeon Kim, Sakura Schafer-Nameki +1
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep01(2020)101
101 pages, 11 figures
arxiv created 2019/10/30 · arxiv updated 2020/02/19
By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d (2,0) theory on a three-manifold M3. This generalization is applicable to both the 3d N=2 and N=1 supersymmetric reductions. An observable that is sensitive to the higher-form symmetries is the Witten index, which can be computed by counting solutions to a set of Bethe equations that are determined by M3. This is carried out in detail for M3 a Seifert manifold, where we compute a refined version of the Witten index. In the context of the 3d-3d correspondence, we complement this analysis in the dual topological theory, and determine the refined counting of flat connections on M3, which matches the Witten index computation that takes the higher-form symmetries into account.