Constructs a family of non-relativistic limits of 4d MSYM via brane setups that organize into a 3D moduli space with nontrivial topology where PSL(2,Z) dualities act more complexly than in the relativistic theory, establishing Abelian duality by path integral and supporting non-Abelian case via spec
Electric-Magnetic Duality And The Geometric Langlands Program
9 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge theory, mirror symmetry of sigma-models, branes, Wilson and 't Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke eigensheaves and D-modules, arise naturally from the physics.
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A D5-D7 brane configuration in AdS5 x S5 provides an interpolating holographic dual for defect CFTs, with anomaly cancellation and a conjectured SYM solution.
Tropicalization of exact WKB formulae for NRS coordinates on the four-punctured sphere yields chamberwise agreement with Seiberg-Witten periods of SU(2) Nf=4 in unimodular primitive-symplectic chambers.
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
Refines charge quantization via homotopy type A whose homotopy groups classify brane charges and homology groups classify higher-form symmetries, deriving swampland-like constraints that rule out noncompact gauge groups and non-nilpotent Lie algebras for field strengths.
Equidistribution of Hecke operators in large N CFT limits reduces the partition function to light-state Poincaré series with an immediate interpretation as sums over handlebody geometries.
Holographic co-dimension-two defect CFTs have type-A Weyl anomaly coefficient b negative in a finite parameter region, with weak–strong agreement for type-A and type-B coefficients in a limit.
Monodromy defects in Maxwell theory are analyzed via mapping to hyperbolic space, recovering the defect primary spectrum and showing that Wilson/'t Hooft lines terminate on defects, become decomposable, and follow Chern-Simons topological behavior.
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.
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Non-relativistic limits of $\mathcal N=4$ supersymmetric Yang-Mills theory and S-duality
Constructs a family of non-relativistic limits of 4d MSYM via brane setups that organize into a 3D moduli space with nontrivial topology where PSL(2,Z) dualities act more complexly than in the relativistic theory, establishing Abelian duality by path integral and supporting non-Abelian case via spec
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Holographic interpolations of defect CFTs
A D5-D7 brane configuration in AdS5 x S5 provides an interpolating holographic dual for defect CFTs, with anomaly cancellation and a conjectured SYM solution.
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Tropical WKB asymptotics of NRS coordinates for opers in $SU(2)$, $N_f=4$ theory
Tropicalization of exact WKB formulae for NRS coordinates on the four-punctured sphere yields chamberwise agreement with Seiberg-Witten periods of SU(2) Nf=4 in unimodular primitive-symplectic chambers.
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Semiorthogonal decompositions for stacks
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
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Generalised Symmetries and Swampland-Type Constraints from Charge Quantisation via Rational Homotopy Theory
Refines charge quantization via homotopy type A whose homotopy groups classify brane charges and homology groups classify higher-form symmetries, deriving swampland-like constraints that rule out noncompact gauge groups and non-nilpotent Lie algebras for field strengths.
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Holographic Equidistribution
Equidistribution of Hecke operators in large N CFT limits reduces the partition function to light-state Poincaré series with an immediate interpretation as sums over handlebody geometries.
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Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling
Holographic co-dimension-two defect CFTs have type-A Weyl anomaly coefficient b negative in a finite parameter region, with weak–strong agreement for type-A and type-B coefficients in a limit.
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Monodromy Defects for Electric-Magnetic Duality, Hyperbolic Space, and Lines
Monodromy defects in Maxwell theory are analyzed via mapping to hyperbolic space, recovering the defect primary spectrum and showing that Wilson/'t Hooft lines terminate on defects, become decomposable, and follow Chern-Simons topological behavior.
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Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.