Derives weakest quantization conditions in terms of monodromy data for higher-order DEs tied to quantum Toda chain and proves duality predictions for deformed Schrödinger operators.
Defects and Quantum Seiberg-Witten Geometry
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study the Nekrasov partition function of the five dimensional U(N) gauge theory with maximal supersymmetry on R^4 x S^1 in the presence of codimension two defects. The codimension two defects can be described either as monodromy defects, or by coupling to a certain class of three dimensional quiver gauge theories on R^2 x S^1. We explain how these computations are connected with both classical and quantum integrable systems. We check, as an expansion in the instanton number, that the aforementioned partition functions are eigenfunctions of an elliptic integrable many-body system, which quantizes the Seiberg-Witten geometry of the five-dimensional gauge theory.
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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.
Schubert line defects in 3d GLSMs for complete flag manifolds are realized as SQM quivers whose indices give quantum Grothendieck polynomials and restrict the target space to Schubert varieties.
Dimer graphs are constructed for relativistic Toda chains of listed Lie algebra types, and Seiberg-Witten curves of 5d N=1 pure SYM for group G are identified as spectral curves of the dual Toda chain for G^vee.
Fluid dynamics is formulated as an intersection problem on a symplectic manifold associated with spacetime, yielding a geometric derivation of covariant hydrodynamics and extensions to multicomponent and anomalous fluids.
Continuous-universe decomposition plus (-1)-form gauging eliminates every instanton in local QFTs, realized explicitly by switching 2D U(1) gauge theories to noncompact R gauge groups.
Generalized Schur indices of N=2 class S theories are expressed using eigenfunctions of non-relativistic elliptic Calogero-Moser models, with extensions claimed for N=1 SCFTs via limits of models like Inozemtsev.
citing papers explorer
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Higher-Rank Connections and Deformed Schr\"odinger Operators
Derives weakest quantization conditions in terms of monodromy data for higher-order DEs tied to quantum Toda chain and proves duality predictions for deformed Schrödinger operators.
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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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Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials
Schubert line defects in 3d GLSMs for complete flag manifolds are realized as SQM quivers whose indices give quantum Grothendieck polynomials and restrict the target space to Schubert varieties.
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Dimers for Relativistic Toda Models with Reflective Boundaries
Dimer graphs are constructed for relativistic Toda chains of listed Lie algebra types, and Seiberg-Witten curves of 5d N=1 pure SYM for group G are identified as spectral curves of the dual Toda chain for G^vee.
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Fluid dynamics as intersection problem
Fluid dynamics is formulated as an intersection problem on a symplectic manifold associated with spacetime, yielding a geometric derivation of covariant hydrodynamics and extensions to multicomponent and anomalous fluids.
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Total instanton restriction via multiverse interference: Noncompact gauge theories and (-1)-form symmetries
Continuous-universe decomposition plus (-1)-form gauging eliminates every instanton in local QFTs, realized explicitly by switching 2D U(1) gauge theories to noncompact R gauge groups.
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On non-relativistic integrable models and 4d SCFTs
Generalized Schur indices of N=2 class S theories are expressed using eigenfunctions of non-relativistic elliptic Calogero-Moser models, with extensions claimed for N=1 SCFTs via limits of models like Inozemtsev.