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Twisted indices of 3d N = 4 gauge theories and enumerative geometry of quasi-maps

Bullimore, Mathew; Ferrari, Andrea; Kim, Heeyeon

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Authors

Andrea Ferrari

Heeyeon Kim



Abstract

We explore the geometric interpretation of the twisted index of 3d N = 4 gauge theories on S 1 × Σ where Σ is a closed Riemann surface. We focus on a rich class of supersymmetric quiver gauge theories that have isolated vacua under generic mass and FI parameter deformations. We show that the path integral localises to a moduli space of solutions to generalised vortex equations on Σ, which can be understood algebraically as quasi-maps to the Higgs branch. We show that the twisted index reproduces the virtual Euler characteristic of the moduli spaces of twisted quasi-maps and demonstrate that this agrees with the contour integral representation introduced in previous work. Finally, we investigate 3d N = 4 mirror symmetry in this context, which implies an equality of enumerative invariants associated to mirror pairs of Higgs branches under the exchange of equivariant and degree counting parameters.

Citation

Bullimore, M., Ferrari, A., & Kim, H. (2019). Twisted indices of 3d N = 4 gauge theories and enumerative geometry of quasi-maps. Journal of High Energy Physics, 2019(7), Article 14. https://doi.org/10.1007/jhep07%282019%29014

Journal Article Type Article
Acceptance Date Jun 26, 2019
Online Publication Date Jul 3, 2019
Publication Date Jul 31, 2019
Deposit Date Jul 24, 2019
Publicly Available Date Mar 28, 2024
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2019
Issue 7
Article Number 14
DOI https://doi.org/10.1007/jhep07%282019%29014

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is distributed under the terms of the Creative Commons
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.





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