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Interfaces and Quantum Algebras, I: Stable Envelopes
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Interfaces and Quantum Algebras, I: Stable Envelopes
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The stable envelopes of Okounkov et al. realize some representations of quantum algebras associated to quivers, using geometry. We relate these geometric considerations to quantum field theory. The main ingredients are the supersymmetric interfaces in gauge theories with four supercharges, relation of supersymmetric vacua to generalized cohomology theories, and Berry connections. We mainly consider softly broken compactified three dimensional $\mathcal{N} =4$ theories. The companion papers will discuss applications of this construction to symplectic duality, Bethe/gauge correspondence, generalizations to higher dimensional theories, and other topics.
Forward citations
Cited by 3 Pith papers
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Meromorphic amplitudes from 3-dimensional supersymmetry
Coon amplitude equals 3d N=2 half-index of XYZ model with boundary conditions; IR flow gives Veneziano amplitude, and elliptic completion of q^ST yields a meromorphic positive version.
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Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials
Schubert line defects in 3d GLSMs for partial flag manifolds reproduce parabolic Whitney polynomials for Schubert classes in quantum K-theory and yield new parabolic quantum Grothendieck polynomials.
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On the Schubert calculus of the quantum K-theory for partial flag manifolds: a 3d A-model perspective
Computes 2- and 3-point functions of Schubert line defects in 3d A-model for partial flag manifolds Fl(k;n) to obtain K-theoretic Littlewood-Richardson coefficients, with small-beta limit recovering 2d quantum cohomology.
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