2021
DOI: 10.48550/arxiv.2109.10907
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3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve

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 c… Show more

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Cited by 3 publications
(3 citation statements)
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References 72 publications
(163 reference statements)
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“…These different brane webs are different phases (chambers) of 3d theories. Notice that some mass parameters between two chambers have opposite signs, which is similar to the interface discussed in [55,62,63].…”
Section: Real Mass Deformationssupporting
confidence: 62%
“…These different brane webs are different phases (chambers) of 3d theories. Notice that some mass parameters between two chambers have opposite signs, which is similar to the interface discussed in [55,62,63].…”
Section: Real Mass Deformationssupporting
confidence: 62%
“…Meanwhile, the R-matrices on highest-weight modules admit a geometric construction from stable envelopes [99,100]. The stable envelope was realized in the context of the Bethe/gauge correspondence by the Janus interface interpolating different values of real masses [6,[101][102][103]. It would be interesting to extend this gauge theoretical construction of the stable envelopes so that the R-matrices on bi-infinite modules would be incorporated, perhaps by regarding the C ε 2 -plane as a cigar and compactifying along its circle fiber.…”
Section: Yangian Double and Quantum Vertex Algebramentioning
confidence: 99%
“…Half-BPS boundary conditions can preserve either N ¼ ð1; 1Þ which have been described in [35,36], or N ¼ ð0; 2Þ which we focus here. In particular, N ¼ ð0; 2Þ half-BPS chiral UV boundary conditions preserving the Uð1Þ R symmetry lead to various applications [35,[37][38][39][40][41][42][43][44][45][46][47]. For pairs of UV boundary conditions, there exist dual boundary conditions which flow to the same IR boundary conditions.…”
Section: Introduction and Conclusionmentioning
confidence: 99%