Circular quiver gauge theories, isomonodromic deformations and $$W_N$$ fermions on the torus

Bonelli, Giulio; Monte, Fabrizio Del; Gavrylenko, Pavlo; Tanzini, Alessandro

doi:10.1007/s11005-020-01343-4

Cited by 7 publications

(9 citation statements)

References 83 publications

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“…• Our analysis can be extended to irregular blocks on Riemann surfaces of higher genus. For example the genus one case is related to circular quiver gauge theories [59,60] • By considering BPZ equations corresponding to higher level degenerate vertices, one can extend our analysis to higher order linear ODEs with rational coefficients.…”

Section: Introductionmentioning

confidence: 99%

Irregular Liouville correlators and connection formulae for Heun functions

Bonelli¹,

Iossa²,

Lichtig³

et al. 2022

Preprint

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We perform a detailed study of a class of irregular correlators in Liouville Conformal Field Theory, of the related Virasoro conformal blocks with irregular singularities and of their connection formulae. Upon considering their semi-classical limit, we provide explicit expressions of the connection matrices for the Heun function and a class of its confluences. Their calculation is reduced to concrete combinatorial formulae from conformal block expansions.

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Section: Introductionmentioning

confidence: 99%

Irregular Liouville correlators and connection formulae for Heun functions

Bonelli¹,

Iossa²,

Lichtig³

et al. 2022

Preprint

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“…3, V a+n/2 is the Virasoro Verma module with dimension (a + n/2) 2 , V m (0) is a Virasoro primary field inserted on the torus at the origin in cylindrical coordinates, and q = e 2πiτ . The general statement for higher rank and arbitrary number of regular punctures will be discussed in an upcoming paper [35].…”

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confidence: 99%

$${\mathcal {N}}$$ = $$2^*$$ Gauge Theory, Free Fermions on the Torus and Painlevé VI

Bonelli

Monte

Gavrylenko

et al. 2020

Commun. Math. Phys.

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In this paper we study the extension of Painlevé/gauge theory correspondence to circular quivers by focusing on the special case of SU (2) N = 2 * theory. We show that the Nekrasov-Okounkov partition function of this gauge theory provides an explicit combinatorial expression and a Fredholm determinant formula for the tau-function describing isomonodromic deformations of SL 2 flat connections on the one-punctured torus. This is achieved by reformulating the Riemann-Hilbert problem associated to the latter in terms of chiral conformal blocks of a free-fermionic algebra. This viewpoint provides the exact solution of the renormalization group flow of the SU (2) N = 2 * theory on self-dual Ωbackground and, in the Seiberg-Witten limit, an elegant relation between the IR and UV gauge couplings.

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“…• Isomonodromy problems, as it is now known that conformal blocks (and hence Nekrasov partition functions), Fourier transformed with respect to internal momenta, give solutions to Painlevé equations arising in isomonodromy problems for Fuchsian connections [181,286,290,293,417,633,650,672,716,730,808,826,837,838,56 Reference lists are both less complete and less properly filtered here than elsewhere in the review. 878,891,; likewise the chiral blocks of the q-deformed Virasoro algebra and qW-algebras give solutions of q-Painlevé equations [453][454][455].…”

Section: Discussionmentioning

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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Circular quiver gauge theories, isomonodromic deformations and $$W_N$$ fermions on the torus

Cited by 7 publications

References 83 publications

Irregular Liouville correlators and connection formulae for Heun functions

Irregular Liouville correlators and connection formulae for Heun functions

$${\mathcal {N}}$$ = $$2^*$$ Gauge Theory, Free Fermions on the Torus and Painlevé VI

A slow review of the AGT correspondence

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