Comments on twisted indices in 3d supersymmetric gauge theories

Journal article

We study three-dimensional N = 2 supersymmetric gauge theories on Σg × S 1 with a topological twist along Σg, a genus-g Riemann surface. The twisted supersymmetric index at genus g and the correlation functions of half-BPS loop operators on S 1 can be computed exactly by supersymmetric localization. For g = 1, this gives a simple UV computation of the 3d Witten index. Twisted indices provide us with a clean derivation of the quantum algebra of supersymmetric Wilson loops, for any Yang-Mills-Chern-Simonsmatter theory, in terms of the associated Bethe equations for the theory on R 2 × S 1 . This also provides a powerful and simple tool to study 3d N = 2 Seiberg dualities. Finally, we study A- and B-twisted indices for N = 4 supersymmetric gauge theories, which turns out to be very useful for quantitative studies of three-dimensional mirror symmetry. We also briefly comment on a relation between the S 2 × S 1 twisted indices and the Hilbert series of N = 4 moduli spaces.

Authors: Closset, C; Kim, H

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer Berlin Heidelberg
• Journal: Journal of High Energy Physics
• Volume: 2016
• Issue: 8
• Article number: 59
• Publication date: 2016-08-09
• Acceptance date: 2016-07-31
• DOI: 10.1007/JHEP08(2016)059
• ISSN: 1029-8479
• Keywords: Field theories in lower dimensions; Wilson; supersymmetric gauge theory; supersymmetry and duality; ’t Hooft and Polyakov loops