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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Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
23 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category ("number of BPS states with given charge" in physics language). Formally, our motivic DT-invariants are elements of quantum tori over a version of the Grothendieck ring of varieties over the ground field. Via the quasi-classical limit "as the motive of affine line approaches to 1" we obtain numerical DT-invariants which are closely related to those introduced by Behrend. We study some properties of both motivic and numerical DT-invariants including the wall-crossing formulas and integrality. We discuss the relationship with the mathematical works (in the non-triangulated case) of Joyce, Bridgeland and Toledano-Laredo, as well as with works of physicists on Seiberg-Witten model (string junctions), classification of N=2 supersymmetric theories (Cecotti-Vafa) and structure of the moduli space of vector multiplets. Relating the theory of 3d Calabi-Yau categories with distinguished set of generators (called cluster collection) with the theory of quivers with potential we found the connection with cluster transformations and cluster varieties (both classical and quantum).
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representative citing papers
Links resurgence of the topological string partition function to DT wall-crossing via an isomorphism of alien derivative algebras to the Kontsevich-Soibelman Lie algebra, with Borel singularities matched to specific DT invariants.
Vertices of fundamental domains for del Pezzo quantum curves with FI parameters are realized as factorized curves from 5-branes dressed by FI parameters, matching minuscule weights.
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.
Authors propose shaded A-polynomials A_a(ℓ_b, m_c) for SU(N) via CG chords from huge representations of U_q(su_N) in the classical limit, with examples for knots 3_1, 4_1, 5_1 in su_3.
New proof of Ishii's conjecture for dihedral reflection groups via Bridgeland stability conditions on root stacks of maximal resolutions.
Numerical analysis of 5D indices shows a transition from BMPV black hole entropy to black ring entropy at critical angular momentum m, while PT invariants exhibit two further transitions at positive m and DT invariants transition to D0-brane dominance.
A birational Weyl group action on the cluster A_n-quiver has as its Poisson invariants exactly the formal geodesic functions (matrix entries), yielding transitive Hamiltonian reductions on the geometric leaf and an even/odd parity dichotomy for cluster DT-transformations.
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.
Construction of the scattering diagram for BPS indices on local P1 x P1 and sketch of the Split Attractor Flow Tree Conjecture for restricted central charge phase.
Using Hom-infinite Frobenius categorification of the Grassmannian, the authors determine g-vectors of Plücker coordinates for the triangular seed and express DT F-polynomials in terms of 3D Young diagrams, giving a new proof of Weng's theorem.
Extends operator formalism of closed topological strings to derive all-order trans-series solutions for real topological strings, with disk invariants as Stokes constants and numerical checks on local P2.
In the classical strong-coupling regime, half-BPS correlation functions in planar N=4 SYM exponentiate under the hexagon formalism and are governed by TBA equations structurally equivalent to Gaiotto-Moore-Neitzke equations, enabling a chi-system for both polygonal and closed geometries.
A projection of the variation morphism defines an intersection-space Hodge atom shadow package for Calabi-Yau conifolds, yielding a middle-degree IC-intersection-space defect of rank 202 for the 125-node quintic.
A modal phase-matching scheme using TM20-to-TE00 mode conversion enables poling-free SPDC in 4H-SiC and lithium niobate on-insulator waveguides with simulated conversion efficiencies of 96-99%.
PT generating functions with descendents are rational, with controlled poles, for superpositive curve classes on projective complex 3-folds.
Stokes constants of topological string non-perturbative contributions are invariant on monodromy orbits, reproduce the BPS spectrum, and satisfy the Kontsevich-Soibelman Lie algebra.
A new proof of Li's theorem on geometric Bridgeland stability conditions on projective spaces is given via quotient stack restriction.
Claims a unified geometric framework relating split attractor flow, Hessian flow, and spectral networks, but the central duality proof is incomplete and key formulas are internally inconsistent.
Motivic Hall algebra geometry and moduli stack correspondences recover Auslander-Reiten sequences and the Auslander-Reiten quiver.
Lecture notes summarizing recent progress on hyper-Kähler varieties via Lagrangian fibrations, atomic sheaves, and derived categories.
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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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The non-perturbative topological string: from resurgence to wall-crossing of DT invariants
Links resurgence of the topological string partition function to DT wall-crossing via an isomorphism of alien derivative algebras to the Kontsevich-Soibelman Lie algebra, with Borel singularities matched to specific DT invariants.
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Factorized Quantum Curves and Minuscule Vertices in 3D Duality Cascades with FI Parameters
Vertices of fundamental domains for del Pezzo quantum curves with FI parameters are realized as factorized curves from 5-branes dressed by FI parameters, matching minuscule weights.
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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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Shading A-polynomials via huge representations of $U_q(\mathfrak{su}_N)$
Authors propose shaded A-polynomials A_a(ℓ_b, m_c) for SU(N) via CG chords from huge representations of U_q(su_N) in the classical limit, with examples for knots 3_1, 4_1, 5_1 in su_3.
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Ishii's conjecture and Bridgeland stability conditions for dihedral reflection groups
New proof of Ishii's conjecture for dihedral reflection groups via Bridgeland stability conditions on root stacks of maximal resolutions.
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Large Order Enumerative Geometry, Black Holes and Black Rings
Numerical analysis of 5D indices shows a transition from BMPV black hole entropy to black ring entropy at critical angular momentum m, while PT invariants exhibit two further transitions at positive m and DT invariants transition to D0-brane dominance.
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Birational Weyl Group Action on the Symplectic Groupoid and Cluster Algebras
A birational Weyl group action on the cluster A_n-quiver has as its Poisson invariants exactly the formal geodesic functions (matrix entries), yielding transitive Hamiltonian reductions on the geometric leaf and an even/odd parity dichotomy for cluster DT-transformations.
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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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BPS Dendroscopy on Local $\mathbb{P}^1\times \mathbb{P}^1$
Construction of the scattering diagram for BPS indices on local P1 x P1 and sketch of the Split Attractor Flow Tree Conjecture for restricted central charge phase.
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$g$-vectors and $DT$-$F$-polynomials for Grassmannians
Using Hom-infinite Frobenius categorification of the Grassmannian, the authors determine g-vectors of Plücker coordinates for the triangular seed and express DT F-polynomials in terms of 3D Young diagrams, giving a new proof of Weng's theorem.
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Non-Perturbative Real Topological Strings
Extends operator formalism of closed topological strings to derive all-order trans-series solutions for real topological strings, with disk invariants as Stokes constants and numerical checks on local P2.
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Classical correlation functions at strong coupling from hexagonalization
In the classical strong-coupling regime, half-BPS correlation functions in planar N=4 SYM exponentiate under the hexagon formalism and are governed by TBA equations structurally equivalent to Gaiotto-Moore-Neitzke equations, enabling a chi-system for both polygonal and closed geometries.
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Defect Triangles and Intersection-Space Hodge Atom Shadows for Calabi--Yau Conifolds
A projection of the variation morphism defines an intersection-space Hodge atom shadow package for Calabi-Yau conifolds, yielding a middle-degree IC-intersection-space defect of rank 202 for the 125-node quintic.
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A Riemann-Hilbert correspondence for cohomology theories of closed 1-forms
A modal phase-matching scheme using TM20-to-TE00 mode conversion enables poling-free SPDC in 4H-SiC and lithium niobate on-insulator waveguides with simulated conversion efficiencies of 96-99%.
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The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds
PT generating functions with descendents are rational, with controlled poles, for superpositive curve classes on projective complex 3-folds.
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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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A note on stability conditions on projective spaces
A new proof of Li's theorem on geometric Bridgeland stability conditions on projective spaces is given via quotient stack restriction.
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Geometry of BPS Attractor, Hessian, and Spectral Flows
Claims a unified geometric framework relating split attractor flow, Hessian flow, and spectral networks, but the central duality proof is incomplete and key formulas are internally inconsistent.
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Hall Geometry and Auslander-Reiten Quiver
Motivic Hall algebra geometry and moduli stack correspondences recover Auslander-Reiten sequences and the Auslander-Reiten quiver.
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Hyper-K\"ahler varieties: Lagrangian fibrations, atomic sheaves, and categories
Lecture notes summarizing recent progress on hyper-Kähler varieties via Lagrangian fibrations, atomic sheaves, and derived categories.
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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.