Professor Mathew Bullimore mathew.r.bullimore@durham.ac.uk
Professor
3d N = 4 Gauge Theories on an Elliptic Curve
Bullimore, Mathew; Zhang, Daniel
Authors
Daniel Zhang
Abstract
This paper studies 3d N = 4 supersymmetric gauge theories on an elliptic curve, with the aim to provide a physical realisation of recent constructions in equivariant elliptic cohomology of symplectic resolutions. We first study the Berry connection for supersymmetric ground states in the presence of mass parameters and flat connections for flavour symmetries, which results in a natural construction of the equivariant elliptic cohomology variety of the Higgs branch. We then investigate supersymmetric boundary conditions and show from an analysis of boundary ’t Hooft anomalies that their boundary amplitudes represent equivariant elliptic cohomology classes. We analyse two distinguished classes of boundary conditions known as exceptional Dirichlet and enriched Neumann, which are exchanged under mirror symmetry. We show that the boundary amplitudes of the latter reproduce elliptic stable envelopes introduced by Aganagic-Okounkov, and relate boundary amplitudes of the mirror symmetry interface to the mother function in equivariant elliptic cohomology. Finally, we consider correlation functions of Janus interfaces for varying mass parameters, recovering the chamber R-matrices of elliptic integrable systems.
Citation
Bullimore, M., & Zhang, D. (2022). 3d N = 4 Gauge Theories on an Elliptic Curve. SciPost Physics, 13(1), Article 005. https://doi.org/10.21468/scipostphys.13.1.005
Journal Article Type | Article |
---|---|
Acceptance Date | Jun 1, 2022 |
Online Publication Date | Jul 22, 2022 |
Publication Date | 2022-07 |
Deposit Date | Sep 5, 2022 |
Publicly Available Date | Sep 5, 2022 |
Journal | SciPost Physics |
Print ISSN | 2542-4653 |
Electronic ISSN | 2542-4653 |
Publisher | SciPost |
Peer Reviewed | Peer Reviewed |
Volume | 13 |
Issue | 1 |
Article Number | 005 |
DOI | https://doi.org/10.21468/scipostphys.13.1.005 |
Public URL | https://durham-repository.worktribe.com/output/1195763 |
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
This work is licensed under the Creative Commons Attribution 4.0 International License.
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