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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Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
16 Pith papers cite this work. Polarity classification is still indexing.
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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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UNVERDICTED 16representative citing papers
Introduces birational Weyl group action on symplectic groupoid of A_n matrices via cluster transformations and proves invariants form finite central extension of matrix entry algebra, with applications to Teichmuller images and DT-transformations.
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 study of high-genus GV invariants reveals 5D indices matching BMPV black-hole entropy below a critical angular momentum and black-ring dominance above, with additional phase transitions and growth laws in PT and DT invariants.
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.
Establishes a Deligne-Malgrange Riemann-Hilbert correspondence for closed 1-forms and a variant comparison of isomorphisms theorem for simple algebraic 1-forms on complex curves.
Proves that generating functions of Pandharipande-Thomas invariants with descendent insertions are rational with controlled poles for superpositive curve classes on projective complex 3-manifolds.
Lecture notes summarizing recent progress on hyper-Kähler varieties via Lagrangian fibrations, atomic sheaves, and derived categories.
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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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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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.