Interfaces and Quantum Algebras, I: Stable Envelopes

Dedushenko, Mykola; Nekrasov, Nikita

doi:10.48550/arxiv.2109.10941

Cited by 9 publications

(20 citation statements)

References 169 publications

(283 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%

3d $$ \mathcal{N} $$ = 2 brane webs and quiver matrices

Cheng

2022

J. High Energ. Phys.

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We discuss 3d brane webs and effective Chern-Simons levels for 3d $$ \mathcal{N} $$ N = 2 gauge theories. We find that turning on real masses for chiral multiplets leads to various equivalent brane webs that are related by flipping positions of D5-branes. We interpret flips as ST-transformations for chiral multiplets. ST-transformations could turn abelian theories into dual theories with mixed Chern-Simons levels that are interpreted as quiver matrices Cij encoding DT-invariants. We notice that each brane web corresponds to a quiver matrix. ST-transformations of holomorphic blocks are discussed to verify results. We also discuss the movement of flavor D5-branes, which leads to double-layer brane webs and manifests fiber-base duality. In the second part, we compute refined vortex partition functions of nonabelian theories with the gauge group U(N) and find corresponding quiver matrices. The computation shows that on Higgs branch nonabelian groups are broken to abelian groups.

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Section: Real Mass Deformationssupporting

confidence: 62%

3d $$ \mathcal{N} $$ = 2 brane webs and quiver matrices

Cheng

2022

J. High Energ. Phys.

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“…Note added: in the process of completing this project we became aware of related ongoing work of Mykola Dedushenko and Nikita Nekrasov [22], and we are grateful to them for agreeing to coordinate the release.…”

Section: Enriched Neumannmentioning

confidence: 99%

3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve

Bullimore

Zhang

2022

SciPost Phys.

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This paper studies 3d3d\mathcal{N}=4𝒩=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.

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“…OPE's of line defects have also played an important role in the geometric Langlands program [64]. Recently there have been some investigations into the "operator product expansions" of surface defects [115] and interfaces [305], finding interesting relations to homotopy algebra and infinite-dimensional quantum algebras. It seems clear that there is a rich mathematical structure to be discovered here.…”

Section: Defectsmentioning

confidence: 99%

“…The whole structure resembles a Lie algebra, or its Yangian, or quantum, deformation, as seen in the context of gauge theories with (4,4) supersymmetry in two dimensions. For the recent progress see [305]. These developments are partly based on the mathematical discoveries in [337,338].…”

Section: Defectsmentioning

confidence: 99%

A Panorama Of Physical Mathematics c. 2022

Bah¹,

Freed²,

Moore³

et al. 2022

Preprint

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What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forwardlooking, suggesting potentially useful and fruitful directions and problems, some old, some new, for further development of the subject. This paper is a much extended version of the Snowmass whitepaper on physical mathematics [1].

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Interfaces and Quantum Algebras, I: Stable Envelopes

Cited by 9 publications

References 169 publications

3d $$ \mathcal{N} $$ = 2 brane webs and quiver matrices

3d $$ \mathcal{N} $$ = 2 brane webs and quiver matrices

3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve

A Panorama Of Physical Mathematics c. 2022

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