Non-perturbative approaches to the quantum Seiberg-Witten curve

Grassi, Alba; Gu, Jie; Mariño, Marcos

doi:10.1007/jhep07(2020)106

Cited by 61 publications

(119 citation statements)

References 105 publications

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“…We have also shown that the X-cluster variables correctly reproduce the ones of the four-dimensional BPS quivers under a suitable scaling limit. It would be very interesting to further explore the relation of our results with the ones on exact WKB methods and TBA equations [56,66,67], possibly extending these methods to the q-difference/5d case. For the class S theories, an important rôle should be played by the group Hitchin system [68], in the perspective of its quantization [69,70].…”

Section: Discussionmentioning

confidence: 88%

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BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations

Bonelli

Monte

Tanzini

2021

Ann. Henri Poincaré

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We study the discrete flows generated by the symmetry group of the BPS quivers for Calabi–Yau geometries describing five-dimensional superconformal quantum field theories on a circle. These flows naturally describe the BPS particle spectrum of such theories and at the same time generate bilinear equations of q-difference type which, in the rank one case, are q-Painlevé equations. The solutions of these equations are shown to be given by grand canonical topological string partition functions which we identify with $$\tau $$ τ -functions of the cluster algebra associated to the quiver. We exemplify our construction in the case corresponding to five-dimensional SU(2) pure super Yang–Mills and $$N_f=2$$ N f = 2 on a circle.

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Section: Discussionmentioning

confidence: 88%

“…A first instance of this phenomenon was discussed from the mathematical perspective in [55]. For the case at hand, the non-trivial relation between the two approaches is encoded in a suitable limit of blow-up equations [43,[56][57][58][59].…”

Section: Discussionmentioning

confidence: 99%

BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations

Bonelli

Monte

Tanzini

2021

Ann. Henri Poincaré

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“…The specific choice of prefactor in (3.29) ensures a simple form of large θ asymptotic behavior for X: In [41,42] it was noticed that the Floquet exponent in the context of N = 2 SYM coincides with the A-cycle period a.…”

Section: Explicit Demonstration Of the Numerical Approachmentioning

confidence: 99%

Recursion relation for instanton counting for SU(2) $$ \mathcal{N} $$ = 2 SYM in NS limit of Ω background

Poghosyan

2021

J. High Energ. Phys.

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In this paper we investigate different ways of deriving the A-cycle period as a series in instanton counting parameter q for $$ \mathcal{N} $$ N = 2 SYM with up to four antifundamental hypermultiplets in NS limit of Ω background. We propose a new recursive method for calculating the period and demonstrate its efficiency by explicit calculations. The new way of doing instanton counting is more advantageous compared to known standard techniques and allows to reach substantially higher order terms with less effort. This approach is applied for the pure case as well as for the case with several hypermultiplets.In addition we suggest a numerical method for deriving the A-cycle period for arbitrary values of q. In the case when one has no hypermultiplets for the A-cycle an analytic expression for large q asymptotics is obtained using a conjecture by Alexei Zamolodchikov. We demonstrate that this expression is in convincing agreement with the numerical approach.

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“…To complete this computation we use the formula from [13] and transform it to more convenient form using (B. 21 5 Spectral theory meaning of quasiclassical conformal blocks…”

Section: Jhep12(2020)125mentioning

confidence: 99%

“…2η ∈ Z, one gets only decaying solution at z → ∞. Hence, to get normalizable solution of (2.15) one has to impose the condition 2η = k ∈ Z, see also [21,22]. Taking into account (2.43) we see that this condition is nothing but the quantization condition [17] ∂F ∂σ ∈ 2πiZ.…”

Section: Jhep12(2020)125mentioning

confidence: 99%

Irregular conformal blocks, Painlevé III and the blow-up equations

Gavrylenko

Marshakov

Stoyan

2020

J. High Energ. Phys.

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We study the relation of irregular conformal blocks with the Painlevé III3 equation. The functional representation for the quasiclassical irregular block is shown to be consistent with the BPZ equations of conformal field theory and the Hamilton-Jacobi approach to Painlevé III3. It leads immediately to a limiting case of the blow-up equations for dual Nekrasov partition function of 4d pure supersymmetric gauge theory, which can be even treated as a defining system of equations for both c = 1 and c → ∞ conformal blocks. We extend this analysis to the domain of strong-coupling regime where original definition of conformal blocks and Nekrasov functions is not known and apply the results to spectral problem of the Mathieu equations. Finally, we propose a construction of irregular conformal blocks in the strong coupling region by quantization of Painlevé III3 equation, and obtain in this way a general expression, reproducing c = 1 and quasiclassical c → ∞ results as its particular cases. We have also found explicit integral representations for c = 1 and c = −2 irregular blocks at infinity for some special points.

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Non-perturbative approaches to the quantum Seiberg-Witten curve

Cited by 61 publications

References 105 publications

BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations

BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations

Recursion relation for instanton counting for SU(2) $$ \mathcal{N} $$ = 2 SYM in NS limit of Ω background

Irregular conformal blocks, Painlevé III and the blow-up equations

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