Functional Equations of Nekrasov Functions Proposed by Ito, Maruyoshi, and Okuda

Ohkawa, Ryo

doi:10.17323/1609-4514-2020-20-3-531-573

Cited by 6 publications

(7 citation statements)

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“…Here we briefly recall methods developed in [15], and [20] for quiver setting. These are similar to [21], [22], and we will also summarize in [24] in more general setting. (1) If P ⊂ ker w and P = 0, we have P ∩ F ℓ = 0.…”

Section: Mochizuki Methodsmentioning

confidence: 53%

“…In this paper, we study algebraic and geometric aspects of vortex partition functions of 2d N = (2, 2) gauge theories and prove the wall-crossing formula of the 2d N = (2, 2) gauge theories, which establishes the precise relation between wall-crossing phenomena and the formulas in [2,7]. The wall-crossing formula we will derive is regarded as a rational degeneration of the wall-crossing formula in [9] and identical to a finite type version of the wall-crossing formulas in [21,22].…”

Section: Introductionmentioning

confidence: 60%

“…Furthermore these arguments are extended in [20] to various cohomology classes other than 1 using the theory of perverse coherent sheaves. This method also gives functional equations of Nekrasov functions [21], [22].…”

Section: Introductionmentioning

confidence: 99%

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Wall-crossing for vortex partition function and handsaw quiver varierty

Ohkawa¹,

Yoshida²

2022

Preprint

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We investigate vortex partition functions defined from integrals over the handsaw quiver varieties of type A1 via wall-crossing phenomena. We consider vortex partition functions defined by two types of cohomology classes, and get functional equations for each of them. We also give explicit formula for these partition functions. This gives proofs to formula suggested by physicsts. In particular, we obtain geometric interpretation of formulas for multiple hypergeometric functions including rational limit of the Kajihara transformation formula.

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Section: Mochizuki Methodsmentioning

confidence: 53%

Section: Introductionmentioning

confidence: 60%

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Wall-crossing for vortex partition function and handsaw quiver varierty

Ohkawa¹,

Yoshida²

2022

Preprint

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“…[33]) or algebraic geometry (see e.g. [90], [91]) arguments. There is a transparent algebraic method to deduce them from the standard (−1) blowup relations 20 .…”

Section: From Blowup Relationsmentioning

confidence: 99%

Quantum spectral problems and isomonodromic deformations

Bershtein,

Gavrylenko,

Grassi

2021

Preprint

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We develop a self-consistent approach to study the spectral properties of a class of quantum mechanical operators by using the knowledge about monodromies of 2 × 2 linear systems (Riemann-Hilbert correspondence). Our technique applies to a variety of problems, though in this paper we only analyse in detail two examples. First we review the case of the (modified) Mathieu operator, which corresponds to a certain linear system on the sphere and makes contact with the Painlevé III 3 equation. Then we extend the analysis to the 2particle elliptic Calogero-Moser operator, which corresponds to a linear system on the torus. By using the Kiev formula for the isomonodromic tau functions, we obtain the spectrum of such operators in terms of self-dual Nekrasov functions (ǫ 1 + ǫ 2 = 0). Through blowup relations, we also find Nekrasov-Shatashvili type of quantizations (ǫ 2 = 0).In the case of the torus with one regular singularity we obtain certain results which are interesting by themselves. Namely, we derive blowup equations (filling some gaps in the literature) and we relate them to the bilinear form of the isomonodromic deformation equations. In addition, we extract the ǫ 2 → 0 limit of the blowup relations from the regularized action functional and CFT arguments.

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“…Nekrasov partition functions have many generalizations, such as on ALE space [179][180][181][182], spiked instantons [183], and a proposed generalization to 4d N = 1 theories [184].…”

Section: Instantonsmentioning

confidence: 99%

A slow review of the AGT correspondence

Floch¹

2020

Preprint

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Starting with a gentle approach to the Alday-Gaiotto-Tachikawa (AGT) correspondence from its 6d origin, these notes provide a wide survey of the literature on numerous extensions of the correspondence. This is the writeup of the lectures given at the Winter School "YRISW 2020" to appear in a special issue of JPhysA.Class S is a wide class of 4d N = 2 supersymmetric gauge theories (ranging from super-QCD to non-Lagrangian theories) obtained by twisted compactification of 6d N = (2, 0) superconformal theories on a Riemann surface C. This 6d construction yields the Coulomb branch and Seiberg-Witten geometry of class S theories, geometrizes S-duality, and leads to the AGT correspondence, which states that many observables of class S theories are equal to 2d conformal field theory (CFT) correlators. For instance, the four-sphere partition function of 4d N = 2 SU(2) superconformal quiver theories is equal to a Liouville CFT correlator of primary operators.Extensions of the AGT correspondence abound: asymptotically-free gauge theories and Argyres-Douglas (AD) theories correspond to irregular CFT operators, quivers with higher-rank gauge groups and non-Lagrangian tinkertoys such as T N correspond to Toda CFT correlators, and nonlocal operators (Wilson-'t Hooft loops, surface operators, domain walls) correspond to Verlinde networks, degenerate primary operators, braiding and fusion kernels, and Riemann surfaces with boundaries.

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Functional Equations of Nekrasov Functions Proposed by Ito, Maruyoshi, and Okuda

Cited by 6 publications

References 0 publications

Wall-crossing for vortex partition function and handsaw quiver varierty

Wall-crossing for vortex partition function and handsaw quiver varierty

Quantum spectral problems and isomonodromic deformations

A slow review of the AGT correspondence

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