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.
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Seiberg-Witten Prepotential From Instanton Counting
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abstract
Direct evaluation of the Seiberg-Witten prepotential is accomplished following the localization programme suggested some time ago. Our results agree with all low-instanton calculations available in the literature. We present a two-parameter generalization of the Seiberg-Witten prepotential, which is rather natural from the M-theory/five dimensional perspective, and conjecture its relation to the tau-functions of KP/Toda hierarchy.
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representative citing papers
Derives Airy representation for S^3 partition functions in M2-brane theories that exactly matches equivariant topological string predictions and proposes a new CY4 to C x CY3 correspondence via quantum curves.
Deformed quantum mechanics from Seiberg-Witten curves shows phases with real or complex instantons, leading to tunneling suppression at Toda points and anomalous scaling at critical monopole points.
In N=2 SU quiver theories the large-N Hagedorn temperature depends only on quiver length for linear cases and equals that of N=4 SYM for holographic quivers, with a universal lower bound of 1/sqrt(2) on the exponential rate alpha of higher-spin current conservation.
A new shell formula unifies and delivers explicit closed-form expressions plus recursions for instanton partition functions in 5d SYM and multiple gauge origami configurations using arbitrary-dimensional Young diagrams.
Proposes and proves for 5D an expression for charge functions of odd-dimensional partitions whose poles mark addable and removable boxes.
Derives closed 5D partial-wave Raman scattering amplitude via NS functions and computes non-vanishing dynamical ℓ=0 and static ℓ=1 scalar tidal Love numbers with RG running up to O(G²) for STBH.
Quantized Coulomb branch of 4d N=2 Sp(N) theory with given matter content matches spherical DAHA of (C_N^vee, C_N) type, proven for N=1 and conjectured for higher N with 't Hooft loop evidence.
The limit shape in the double-elliptic generalization of the Vershik-Kerov problem is governed by a genus two algebraic curve.
Proposes comet-shaped quiver gauge theories for surface defects with nested instantons in 4D gauge theories on T^2 × T*C_{g,k} and gives conjectural explicit formulae for the virtual equivariant elliptic genus of bundles over nested Hilbert schemes of points on the affine plane.
Blow-up equation prefactors encode cubic 1-form self-anomalies and mixed anomalies of 5d N=1 SCFTs, deciding 2-group vs mixed anomaly structure.
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).
Explicit 11D solutions show flux stabilization of T^4/Z2 moduli in EFT does not match the full theory, with non-Lorentz-invariant deformations stabilizing a mix of volume and shape moduli instead.
Derives Z_{S^1×S^2} ∼ |Z_{S^3_b}|^2 for 3d N=2 SCFTs and links it holographically to supersymmetric AdS4 black hole partition functions, akin to OSV.
Exact large-N and strong-coupling results for Bremsstrahlung function in E-theory and D-theory N=2 SCFTs via matrix models, with closed-form non-perturbative contributions.
Derives exact hypergeometric solutions for static perturbations of 5D Myers-Perry black holes and iteratively computes electromagnetic Love tensors showing lower-to-higher angular momentum mode mixing in the response.
Exact partition functions for N=(2,2) theories on spindles are computed via localisation for both twist and anti-twist, yielding a unified formula.
Quasinormal-mode frequencies of extremal Reissner-Nordström black holes for charged and massive scalar fields are computed through Seiberg-Witten/Nekrasov-Shatashvili quantization.
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.
High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and associated MTCs.
Exact WKB with high-order quantum period computations and Borel-Padé resummation reproduces quasinormal mode frequencies for extremal Reissner-Nordström and Kerr black holes.
A global perturbative potential for the Coulomb branch is derived via zeta regularization of D-terms from KK modes in R^3 x S^1 compactifications of 4d N=1 theories.
Instanton partition functions on the blow-up are given by chamber-dependent contour integrals over super-partitions selected by stability conditions, yielding explicit wall-crossing formulas that recover the Nakajima-Yoshioka blow-up formula.
Stokes constants of topological string non-perturbative contributions are invariant on monodromy orbits, reproduce the BPS spectrum, and satisfy the Kontsevich-Soibelman Lie algebra.
citing papers explorer
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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.
-
$S^3$ partition functions and Equivariant CY$_4 $/CY$_3$ correspondence from Quantum curves
Derives Airy representation for S^3 partition functions in M2-brane theories that exactly matches equivariant topological string predictions and proposes a new CY4 to C x CY3 correspondence via quantum curves.
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Thou shalt not tunnel: Complex instantons and tunneling suppression in deformed quantum mechanics
Deformed quantum mechanics from Seiberg-Witten curves shows phases with real or complex instantons, leading to tunneling suppression at Toda points and anomalous scaling at critical monopole points.
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The CFT Distance Conjecture and Tensionless String Limits in $\mathcal N=2$ Quiver Gauge Theories
In N=2 SU quiver theories the large-N Hagedorn temperature depends only on quiver length for linear cases and equals that of N=4 SYM for holographic quivers, with a universal lower bound of 1/sqrt(2) on the exponential rate alpha of higher-spin current conservation.
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Shell formulas for instantons and gauge origami
A new shell formula unifies and delivers explicit closed-form expressions plus recursions for instanton partition functions in 5d SYM and multiple gauge origami configurations using arbitrary-dimensional Young diagrams.
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Charge functions for odd dimensional partitions
Proposes and proves for 5D an expression for charge functions of odd-dimensional partitions whose poles mark addable and removable boxes.
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5-Dimensional Gravitational Raman Scattering: Scalar Wave Perturbations in Schwarzschild-Tangherlini Spacetime
Derives closed 5D partial-wave Raman scattering amplitude via NS functions and computes non-vanishing dynamical ℓ=0 and static ℓ=1 scalar tidal Love numbers with RG running up to O(G²) for STBH.
-
Quantized Coulomb branch of 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory and spherical DAHA of $(C_N^{\vee}, C_N)$-type
Quantized Coulomb branch of 4d N=2 Sp(N) theory with given matter content matches spherical DAHA of (C_N^vee, C_N) type, proven for N=1 and conjectured for higher N with 't Hooft loop evidence.
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Vershik-Kerov in higher times
The limit shape in the double-elliptic generalization of the Vershik-Kerov problem is governed by a genus two algebraic curve.
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Defects, nested instantons and comet shaped quivers
Proposes comet-shaped quiver gauge theories for surface defects with nested instantons in 4D gauge theories on T^2 × T*C_{g,k} and gives conjectural explicit formulae for the virtual equivariant elliptic genus of bundles over nested Hilbert schemes of points on the affine plane.
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Generalised global symmetries in 5d $\mathcal{N}=1$ theories from the blow-up equations
Blow-up equation prefactors encode cubic 1-form self-anomalies and mixed anomalies of 5d N=1 SCFTs, deciding 2-group vs mixed anomaly structure.
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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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Lost in Translation: Moduli Stabilization from EFT to Eleven Dimensions
Explicit 11D solutions show flux stabilization of T^4/Z2 moduli in EFT does not match the full theory, with non-Lorentz-invariant deformations stabilizing a mix of volume and shape moduli instead.
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Towards OSV in AdS
Derives Z_{S^1×S^2} ∼ |Z_{S^3_b}|^2 for 3d N=2 SCFTs and links it holographically to supersymmetric AdS4 black hole partition functions, akin to OSV.
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Bremsstrahlung function in $\mathcal{N}=2$ SCFTs far beyond the supergravity limit
Exact large-N and strong-coupling results for Bremsstrahlung function in E-theory and D-theory N=2 SCFTs via matrix models, with closed-form non-perturbative contributions.
-
Static electromagnetic Love tensors of 5-dimensional Myers-Perry black holes
Derives exact hypergeometric solutions for static perturbations of 5D Myers-Perry black holes and iteratively computes electromagnetic Love tensors showing lower-to-higher angular momentum mode mixing in the response.
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Localisation of $\mathcal{N} = (2,2)$ theories on spindles of both twists
Exact partition functions for N=(2,2) theories on spindles are computed via localisation for both twist and anti-twist, yielding a unified formula.
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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.
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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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Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and associated MTCs.
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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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Perturbative Coulomb branches on $\mathbb{R}^3\times S^1$: the global D-term potential
A global perturbative potential for the Coulomb branch is derived via zeta regularization of D-terms from KK modes in R^3 x S^1 compactifications of 4d N=1 theories.
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Wall-crossing of Instantons on the Blow-up
Instanton partition functions on the blow-up are given by chamber-dependent contour integrals over super-partitions selected by stability conditions, yielding explicit wall-crossing formulas that recover the Nakajima-Yoshioka blow-up formula.
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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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Les Houches Lectures on Exact WKB Analysis and Painlev\'e Equations
Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.
- A Crash Course in Supersymmetric Field Theory Across Dimensions