BPS States, Torus Links and Wild Character Varieties

Diaconescu, Duiliu-Emanuel; Donagi, Ron; Pantev, Tony

doi:10.1007/s00220-018-3097-9

Cited by 10 publications

(24 citation statements)

References 77 publications

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“…In particular, the LMOV invariants of a knot can be expressed in terms of motivic Donaldson-Thomas invariants of corresponding quiver [122] [123]. See some other recent developments on the refined BPS invariants of knot/link in [124] [125]. It is interesting to consider whether blowup equations exist for such circumstances and whether they are able to determine the knot invariants.…”

Section: Discussionmentioning

confidence: 99%

Blowup equations for refined topological strings

Huang

Sun

Wang

2018

J. High Energ. Phys.

130

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Göttsche-Nakajima-Yoshioka K-theoretic blowup equations characterize the Nekrasov partition function of five dimensional N = 1 supersymmetric gauge theories compactified on a circle, which via geometric engineering correspond to the refined topological string theory on SU (N ) geometries. In this paper, we study the K-theoretic blowup equations for general local Calabi-Yau threefolds. We find that both vanishing and unity blowup equations exist for the partition function of refined topological string, and the crucial ingredients are the r fields introduced in our previous paper. These blowup equations are in fact the functional equations for the partition function and each of them results in infinite identities among the refined free energies. Evidences show that they can be used to determine the full refined BPS invariants of local Calabi-Yau threefolds. This serves an independent and sometimes more powerful way to compute the partition function other t han the refined topological vertex in the A-model and the refined holomorphic anomaly equations in the B-model. We study the modular properties of the blowup equations and provide a procedure to determine all the vanishing and unity r fields from the polynomial part of refined topological string at large radius point. We also find that certain form of blowup equations exist at generic loci of the moduli space. To Sheldon Katz on his 60th anniversary arXiv:1711.09884v2 [hep-th] 9 Nov 2018 7 Blowup equations at generic points of moduli space 70 7.1 Modular transformation 70 7.2 Conifold point 70 7.3 Orbifold point 73 -i -8 Outlook 75 References 79

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Section: Discussionmentioning

confidence: 99%

Blowup equations for refined topological strings

Huang

Sun

Wang

2018

J. High Energ. Phys.

130

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“…As shown in [14,, for sufficiently generic ξ the moduli stack H ss ξ (C, D; α, m, d) is isomorphic to a moduli stack of Bridgeland semistable pure dimension one sheaves F on S ξ with compact support. The topological invariants of these sheaves are…”

Section: Spectral Correspondence and Calabi-yau Threefoldsmentioning

confidence: 95%

“…As shown in detail in [14,Sect. 3.1], the string theoretic construction is based on a spectral correspondence relating the irregular Higgs bundles to dimension one sheaves on a holomorphic symplectic surface S ξ .…”

Section: Spectral Correspondence and Calabi-yau Threefoldsmentioning

confidence: 98%

“…For the purposes of the present paper, it suffices to note that given sufficiently generic parameters (Q, τ ) the resulting Higgs bundle moduli problems admit a specific formulation leading to a natural connection to Calabi-Yau enumerative geometry. This construction as well as its relation to the moduli spaces of [6] is explained in detail in Sections 2.1 and 2.3 of [14]. Very briefly, one employs Higgs bundles with a coefficient line bundle M = K C (D)…”

Section: Higgs Bundles and Wild Non-abelian Hodge Correspondencementioning

confidence: 99%

“…The string theoretic approach has been recently generalized to wild character varieties in [14], providing a physical derivation and a generalization for the results of Hausel, Mereb and Wong [25]. While the geometric framework and the spectral construction of [14] are general, explicit formulas are obtained only for wild character varieties with one singular point on the projective line. The goal of the present paper is to further extend these results to wild character varieties with multiple singular points on higher genus curves.…”

Section: Introductionmentioning

confidence: 99%

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Local curves, wild character varieties, and degenerations

Diaconescu

2018

Communications in Number Theory and Physics

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Conjectural results for cohomological invariants of wild character varieties are obtained by counting curves in degenerate Calabi-Yau threefolds. A conjectural formula for E-polynomials is derived from the Gromov-Witten theory of local Calabi-Yau threefolds with normal crossing singularities. A refinement is also conjectured, generalizing existing results of Hausel, Mereb and Wong as well as recent joint work of Donagi, Pantev and the author for weighted Poincaré polynomials of wild character varieties.

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On character varieties of singular manifolds

González-Prieto

Logares

2023

Res Math Sci

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In this paper, we construct a lax monoidal Topological Quantum Field Theory that computes virtual classes, in the Grothendieck ring of algebraic varieties, of G-representation varieties over manifolds with conic singularities, which we call nodefolds. This construction is valid for any algebraic group G, in any dimension and also in the parabolic setting. In particular, this TQFT allows us to compute the virtual classes of representation varieties over complex singular planar curves. In addition, in the case $$G = \textrm{SL}_{2}(k)$$ G = SL 2 ( k ) , the virtual class of the associated character variety over a nodal closed orientable surface is computed both in the non-parabolic and parabolic scenarios.

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BPS States, Torus Links and Wild Character Varieties

Cited by 10 publications

References 77 publications

Blowup equations for refined topological strings

Blowup equations for refined topological strings

Local curves, wild character varieties, and degenerations

On character varieties of singular manifolds

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