q-form global symmetries generalize ordinary symmetries to higher-dimensional charged objects, leading to new rules for amplitudes, gauging, breaking, and anomaly inflow in quantum field theories.
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Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
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abstract
We study four dimensional $N=2$ supersymmetric gauge theories with matter multiplets. For all such models for which the gauge group is $SU(2)$, we derive the exact metric on the moduli space of quantum vacua and the exact spectrum of the stable massive states. A number of new physical phenomena occur, such as chiral symmetry breaking that is driven by the condensation of magnetic monopoles that carry global quantum numbers. For those cases in which conformal invariance is broken only by mass terms, the formalism automatically gives results that are invariant under electric-magnetic duality. In one instance, this duality is mixed in an interesting way with $SO(8)$ triality.
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The Seiberg–Witten SU(2) solution is formalized in Lean 4 with physical assumptions as named predicates and mathematical consequences as sorry-free theorems, demonstrating a method for auditing non-rigorous physics arguments.
A massive deformation of the T[SU(N)] theory is identified as the 3d SCFT realizing the RG-wall and half-BPS boundaries in 4d N=2 SU(N) SYM.
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.
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.
The distinction between spinor and conjugate spinor matter in 5D SO(2N) gauge theories manifests as different boundary conditions on the Seiberg-Witten curve at O5-plane positions (w=±1).
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.
Lattice computation of Wilson-'t Hooft loops supplies numerical evidence for dyon condensation at theta=2pi in SU(2) Yang-Mills.
Quasinormal-mode frequencies of extremal Reissner-Nordström black holes for charged and massive scalar fields are computed through Seiberg-Witten/Nekrasov-Shatashvili quantization.
Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
A refined Kontsevich-Soibelman operator is conjectured to have trace equal to the Macdonald index for special 4d N=2 SCFTs, yielding closed forms for (A1, g) Argyres-Douglas theories.
Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
Exact WKB with high-order quantum period computations and Borel-Padé resummation reproduces quasinormal mode frequencies for extremal Reissner-Nordström and Kerr black holes.
Derives TBA equations for the higher-order Mathieu equation of the SU(r+1) quantum Seiberg-Witten curve, obtains an analytic effective central charge from Y-function boundary conditions at theta to -infinity, and verifies subleading analytic plus higher-order numerical agreement with WKB expansions.
Ultra-local lattice Maxwell theory with a theta term has exact SL(2,Z) duality after a non-local redefinition of the S-transformation, with Wilson and 't Hooft loops transforming up to a self-linking phase.
Stokes constants of topological string non-perturbative contributions are invariant on monodromy orbits, reproduce the BPS spectrum, and satisfy the Kontsevich-Soibelman Lie algebra.
In these supersymmetric theories, the coupling matrix has floor(N/2) independent constants under S-duality, with one distinguished constant that remains key in asymptotic and instanton regimes.
The hadron spectrum in N=2 SQCD with N_f=2N is given by the spectrum of a non-Abelian string on a 2D N=2 supersymmetric black hole, with a Higgs-to-string phase transition viewed as a conifold transition.
citing papers explorer
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Generalized Global Symmetries
q-form global symmetries generalize ordinary symmetries to higher-dimensional charged objects, leading to new rules for amplitudes, gauging, breaking, and anomaly inflow in quantum field theories.
-
Axioms for physical reasoning: codifying the Seiberg--Witten solution in Lean
The Seiberg–Witten SU(2) solution is formalized in Lean 4 with physical assumptions as named predicates and mathematical consequences as sorry-free theorems, demonstrating a method for auditing non-rigorous physics arguments.
-
Half-BPS Boundaries and the RG-Wall of $\mathcal{N}=2$ $SU(N)$ SYM
A massive deformation of the T[SU(N)] theory is identified as the 3d SCFT realizing the RG-wall and half-BPS boundaries in 4d N=2 SU(N) SYM.
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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.
-
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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Thermodynamic limit for SO(2N) gauge theories with spinors/conjugate spinors
The distinction between spinor and conjugate spinor matter in 5D SO(2N) gauge theories manifests as different boundary conditions on the Seiberg-Witten curve at O5-plane positions (w=±1).
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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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Numerical Hints for Dyon Condensation at $\theta=2\pi$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory
Lattice computation of Wilson-'t Hooft loops supplies numerical evidence for dyon condensation at theta=2pi in SU(2) Yang-Mills.
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Quasinormal Modes of Extremal Reissner-Nordstrom Black Holes via Seiberg-Witten Quantization
Quasinormal-mode frequencies of extremal Reissner-Nordström black holes for charged and massive scalar fields are computed through Seiberg-Witten/Nekrasov-Shatashvili quantization.
-
Generalized Families of QFTs
Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
-
Macdonald Index From Refined Kontsevich-Soibelman Operator
A refined Kontsevich-Soibelman operator is conjectured to have trace equal to the Macdonald index for special 4d N=2 SCFTs, yielding closed forms for (A1, g) Argyres-Douglas theories.
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Quiver Yangians as Coulomb branch algebras
Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
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Exact WKB and Quantum Periods for Extremal Black Hole Quasinormal Modes
Exact WKB with high-order quantum period computations and Borel-Padé resummation reproduces quasinormal mode frequencies for extremal Reissner-Nordström and Kerr black holes.
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TBA equations for $SU(r+1)$ quantum Seiberg-Witten curve: higher-order Mathieu equation
Derives TBA equations for the higher-order Mathieu equation of the SU(r+1) quantum Seiberg-Witten curve, obtains an analytic effective central charge from Y-function boundary conditions at theta to -infinity, and verifies subleading analytic plus higher-order numerical agreement with WKB expansions.
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Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation
Ultra-local lattice Maxwell theory with a theta term has exact SL(2,Z) duality after a non-local redefinition of the S-transformation, with Wilson and 't Hooft loops transforming up to a self-linking phase.
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Modular resurgence of topological string
Stokes constants of topological string non-perturbative contributions are invariant on monodromy orbits, reproduce the BPS spectrum, and satisfy the Kontsevich-Soibelman Lie algebra.
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One constant to rule them all
In these supersymmetric theories, the coupling matrix has floor(N/2) independent constants under S-duality, with one distinguished constant that remains key in asymptotic and instanton regimes.
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Hadrons in $\mathcal{N}=2$ supersymmetric QCD from non-Abelian string on 2D black hole
The hadron spectrum in N=2 SQCD with N_f=2N is given by the spectrum of a non-Abelian string on a 2D N=2 supersymmetric black hole, with a Higgs-to-string phase transition viewed as a conifold transition.
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