Comments on twisted indices in 3d supersymmetric gauge theories

By Cyril Closset, Hee-Cheol Kim. 2016

178 citations recorded by the source corpus.

A bstractWe study three-dimensional N$$ \mathcal{N} $$ = 2 supersymmetric gauge theories on Σg × S1 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 S1 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-Simons-matter theory, in terms of the associated Bethe equations for the theory on ℝ2×S1$$ {\mathbb{R}}^2\times {S}^1 $$. This also provides a powerful and simple tool to study 3d N$$ \mathcal{N} $$ = 2 Seiberg dualities. Finally, we study A- and B-twisted indices for N$$ \mathcal{N} $$ = 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 S2 × S1 twisted indices and the Hilbert series of N$$ \mathcal{N} $$ = 4 moduli spaces.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/77840be5582fa68ab5af5d4b07d7fcb9080f9742

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Citations in the corpus

Supersymmetric partition functions on Riemann surfaces (2016, result): “We have coordinated the release of this note with [21], which has overlap with the material presented here.”
A universal counting of black hole microstates in AdS4 (2017, background): “where the function V was called Bethe potential in [4] and is the Yang-Yang function of an associated integrable system [33, 9].”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “They can be derived by supersymmetric localization, similarly to the three-dimensional case studied in [27]—see also [17, 19, 20, 22, 23, 27].”
Black Holes in 4D N=4 Super-Yang-Mills Field Theory (2018, background): “There, the Bekenstein-Hawking entropy of a class of static dyonic BPS black holes in AdS4 was holographically reproduced in the dual CFT3, via supersymmetric localization [12–14].”