Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence

• Main Authors: Julius Eckhard, Heeyeon Kim, Sakura Schäfer-Nameki, Brian Willett
• Format: Article
• Language: English
• Published: SpringerOpen 2020-01-01
• Series: Journal of High Energy Physics
• Subjects: Discrete Symmetries; Field Theories in Lower Dimensions; M-Theory; Supersymmetric Gauge Theory
• Online Access: https://doi.org/10.1007/JHEP01(2020)101

Abstract 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 M 3. This generalization is applicable to both the 3d N $$ \mathcal{N} $$ = 2 and N $$ \mathcal{N} $$ = 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 M 3. This is carried out in detail for M 3 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 M 3, which matches the Witten index computation that takes the higher-form symmetries into account.