Liouville Correlation Functions from Four-Dimensional Gauge Theories

Alday, Luis F.; Gaiotto, Davide; Tachikawa, Yuji

doi:10.1007/s11005-010-0369-5

Cited by 1,349 publications

(2,774 citation statements)

References 36 publications

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“…In [1], it has been proposed that the n-point conformal block on a torus can be identified with the Nekrasov partition function of N = 2 quiver gauge theory discussed in the previous section. This relation for a torus was further studied in [27,53].…”

Section: From Liouville Theory To Generalized Matrix Modelmentioning

confidence: 99%

“…Before going into it, let us see the remaining parts in (3.15) here. As discussed in [1], the gauge coupling constants q i = exp(2πiτ i ) (i = 1, · · · , n) of the SU(2) n quiver gauge theory is related to the modulus q = exp(2πiτ ) of the torus and the insertion points w i of the n-point function of the Liouville theory as q 1 = e 2πi(w 1 −w 2 ) , q 2 = e 2πi(w 2 −w 3 ) , · · · , q n−1 = e 2πi(w n−1 −wn) , q 1 q 2 · · · q n = q . …”

Section: Jhep01(2011)042mentioning

confidence: 99%

“…discussed in [1] in the large N limit. Furthermore, the factor q −a 2 /g 2 s in (3.15) corresponds to the tree level contribution to the prepotential.…”

Section: Jhep01(2011)042mentioning

confidence: 99%

“…Recently, an interesting conjecture has been proposed in [1] that there are two equivalent ways for describing two M5-branes wrapped on a Riemann surface. One of the ways is a four-dimensional N = 2 superconformal SU(2) quiver gauge theory, which is constructed depending on the number of genus and punctures of the Riemann surface [2,3].…”

Section: Introductionmentioning

confidence: 99%

“…The other is the Liouville theory defined on that Riemann surface. The proposal, which is often called AGT conjecture [1], is that the Nekrasov partition function [4] of such quiver gauge theory can be reproduced by the n-point conformal block of the Virasoro algebra, where n is the number of punctures. This conjecture has been generalized to the higher rank gauge group [5][6][7][8], non-conformal case [9][10][11], and to the case in the presence with the surface and loop operators [12]- [24].…”

Section: Introductionmentioning

confidence: 99%

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Seiberg-Witten curve via generalized matrix model

Maruyoshi

Yagi

2011

J. High Energ. Phys.

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Abstract:We study the generalized matrix model which corresponds to the n-point toric Virasoro conformal block. This describes four-dimensional N = 2 SU(2) n gauge theory with circular quiver diagram by the AGT relation. We first verify that the generalized matrix model is obtained from the perturbative calculation of the Liouville correlation function. We then derive the Seiberg-Witten curve for N = 2 gauge theory as a spectral curve of the generalized matrix model.

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Section: From Liouville Theory To Generalized Matrix Modelmentioning

confidence: 99%

Section: Jhep01(2011)042mentioning

confidence: 99%

“…discussed in [1] in the large N limit. Furthermore, the factor q −a 2 /g 2 s in (3.15) corresponds to the tree level contribution to the prepotential.…”

Section: Jhep01(2011)042mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Seiberg-Witten curve via generalized matrix model

Maruyoshi

Yagi

2011

J. High Energ. Phys.

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Non-perturbative studies of N=2 conformal quiver gauge theories

et al. 2015

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We study N = 2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory construction and via the AGT correspondence. We take particular care in obtaining the detailed relation between the parameters appearing in these descriptions and the physical quantities of the quiver gauge theories. This precise map allows us to efficiently reconstruct the non-perturbative prepotential that encodes the effective IR properties of these theories. We give explicit expressions in the cases n = 1, 2, also in the presence of an Ω-background in the Nekrasov-Shatashvili limit. All our results are successfully checked against those of the direct microscopic evaluation of the prepotentialà la Nekrasov using localization methods.

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Higher‐dimensional gauge theories from string theory

Tomasiello

2016

Fortschritte der Physik

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We review some recent developments regarding supersymmetric field theories in six and five dimensions. In particular, we will describe the classification of supersymmetric six-dimensional theories with a holographic IIA dual; they are "linear quivers" consisting of chains of many SU (or SO/Sp) gauge groups connected by hypermultiplets and tensor multiplets. We will also describe the wider classification of supersymmetric sixdimensional theories that can be engineered in F-theory; these are also chains, but they include exceptional gauge groups and copies of a more exotic "E-string" theory with a single tensor and E 8 flavor symmetry. Finally we discuss some properties of these theories under compactification to lower dimensions.

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Liouville Correlation Functions from Four-Dimensional Gauge Theories

Cited by 1,349 publications

References 36 publications

Seiberg-Witten curve via generalized matrix model

Seiberg-Witten curve via generalized matrix model

Non-perturbative studies of N=2 conformal quiver gauge theories

Higher‐dimensional gauge theories from string theory

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