Trinion conformal blocks from topological strings

Coman, Ioana; Pomoni, Elli; Teschner, J.

doi:10.1007/jhep09(2020)078

Cited by 19 publications

(21 citation statements)

References 69 publications

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“…This result could be reproduced within our algebraic formalism provided that we introduce the dual intertwiner Φ * , also constructed in [11], that is expected to enjoy a similar exchange relation. The trinion theories T N provide another set of interesting toric diagrams [57][58][59]. 12 The algebraic object obtained by gluing intertwiners according to these diagrams is also…”

Section: Discussionmentioning

confidence: 99%

Intertwining operator and integrable hierarchies from topological strings

Bourgine

2021

J. High Energ. Phys.

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In [1], Nakatsu and Takasaki have shown that the melting crystal model behind the topological strings vertex provides a tau-function of the KP hierarchy after an appropriate time deformation. We revisit their derivation with a focus on the underlying quantum W1+∞ symmetry. Specifically, we point out the role played by automorphisms and the connection with the intertwiner — or vertex operator — of the algebra. This algebraic perspective allows us to extend part of their derivation to the refined melting crystal model, lifting the algebra to the quantum toroidal algebra of $$ \mathfrak{gl} $$ gl (1) (also called Ding-Iohara-Miki algebra). In this way, we take a first step toward the definition of deformed hierarchies associated to A-model refined topological strings.

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Section: Discussionmentioning

confidence: 99%

Intertwining operator and integrable hierarchies from topological strings

Bourgine

2021

J. High Energ. Phys.

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“…In this case, the massless dyon determines the A-cycle in the polarization of the Seiberg-Witten curve Σ u . 38 Finally, suppose that T is an intrinsically strongly coupled theory. For example, say T is the E 6 Minahan-Nemeschansky theory.…”

Section: A Geometric Recipementioning

confidence: 99%

“…For theories T with a weakly coupled Lagrangian formulation, this recipe computes the well-known Nekrasov-Shatashvili limit of the Nekrasov partition function with respect to the distinguished Fenchel-Nielsen type network W FN described above. The coordinate x i then corresponds to a complexified Fenchel-Nielsen length parameter, which we will denote 38 One might worry that there is no unique such critical Fock-Goncharov type network nor choice of B-cycle, but these ambiguities just illustrate the SL(2, Z) monodromy around the strong coupling point. 39 Recall that there may be multiple W -abelianizations, corresponding to distinct W -framings.…”

Section: A Geometric Recipementioning

confidence: 99%

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A geometric recipe for twisted superpotentials

Hollands

Rüter

Szabo

2021

J. High Energ. Phys.

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We give a pedagogical introduction to spectral networks and abelianization, as well as their relevance to $$ \mathcal{N} $$ N = 2 supersymmetric field theories in four dimensions. Motivated by a conjecture of Nekrasov-Rosly-Shatashvili, we detail a geometric recipe for computing the effective twisted superpotential for $$ \mathcal{N} $$ N = 2 field theories of class $$ \mathcal{S} $$ S as a generating function of the brane of opers, with respect to the spectral coordinates found from abelianization. We present two new examples, the simplest Argyres-Douglas theory and the pure SU(2) gauge theory, while we conjecture the E-expansion of the effective twisted superpotential for the E6 Minahan-Nemeschansky theory.

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“…The function τ 0 appears as a structure constant of the asymptotic formula for solutions of Painlevé VI equation [17,18]. It it also related to the computation of the topological string partition function [8].…”

Section: Introductionmentioning

confidence: 99%

On the tau function of the hypergeometric equation

Bertola,

Korotkin

2022

Preprint

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The monodromy map for a rank-two system of differential equations with three Fuchsian singularities is classically solved by the Kummer formulae for Gauss' hypergeometric functions. We define the tau-function of such a system as the generating function of the extended monodromy symplectomorphism, using an idea recently developed. This formulation allows us to determine the dependence of the tau-function on the monodromy data. Using the explicit solution of the monodromy problem, the tau-function is then explicitly written in terms of Barnes G-function. In particular, if the Fuchsian singularities are placed to 0, 1 and ∞, this gives the structure constants of the asymptotical formula of Iorgov-Gamayun-Lisovyy for solutions of Painlevé VI equation. Contents 1 Introduction 1 2 Isomonodromic tau-function as generating function of extended monodromy symplectomorphism 3 3 Connection problem for three-point Fuchsian system and hypergeometric function 5 3.

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Trinion conformal blocks from topological strings

Cited by 19 publications

References 69 publications

Intertwining operator and integrable hierarchies from topological strings

Intertwining operator and integrable hierarchies from topological strings

A geometric recipe for twisted superpotentials

On the tau function of the hypergeometric equation

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