Loops and unoriented strings

Harris, Geoffrey

doi:10.1016/0550-3213(91)90382-8

Cited by 7 publications

(11 citation statements)

References 30 publications

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“…Here λ ⊂ (s r ) means λ 1 ≤ s and (λ) ≤ r. Let us consider the case that p (2) n := (1 − u n )y n /(1 − t n ) and denote its function by f (x 1−u 1−t y ). Then we have…”

Section: Q-deformed Liouville Correlation Functionmentioning

confidence: 99%

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Five-Dimensional AGT Relation and the Deformed -Ensemble

Awata

Yamada

2010

Progress of Theoretical Physics

122

141

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“…Here λ ⊂ (s r ) means λ 1 ≤ s and (λ) ≤ r. Let us consider the case that p (2) n := (1 − u n )y n /(1 − t n ) and denote its function by f (x 1−u 1−t y ). Then we have…”

Section: Q-deformed Liouville Correlation Functionmentioning

confidence: 99%

“…18)- 21) Our purpose is to study a 5D extension of the AGT relation with N f = 2N in terms of β-ensemble. The A N −1 type quiver matrix model (the ITEP model) 22) was generalized as a β-ensemble 2) satisfying the W N constraint by Ref. 3).…”

Section: §1 Introductionmentioning

confidence: 99%

Five-Dimensional AGT Relation and the Deformed -Ensemble

Awata

Yamada

2010

Progress of Theoretical Physics

122

141

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“…This matrix model is known as the β-ensemble [57,58,59,60] with It is known that this partition function is related to a non-commutative (or quantum) spectral curve [59]. In this case, the non-commutativity is given by…”

Section: β-Ensemblementioning

confidence: 99%

“…This matrix model is known as the β-ensemble[57,58,59,60] with √ β = −ib. For β = 1/2, 1, 2, it corresponds to the integrations over an orthogonal, hermitian and symplectic matrix respectively.…”

mentioning

confidence: 99%

The Quiver Matrix Model and 2d-4d Conformal Connection

Itoyama

Maruyoshi

Oota

2010

Progress of Theoretical Physics

110

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We review the quiver matrix model (the ITEP model) in the light of the recent progress on 2d-4d connection of conformal field theories, in particular, on the relation between Toda field theories and a class of quiver superconformal gauge theories. On the basis of the CFT representation of the beta deformation of the model, a quantum spectral curve is introduced as << det (x- i g_s \partial \phi(z)) >>=0 at finite N and for beta \neq 1. The planar loop equation in the large N limit follows with the aid of W_n constraints. Residue analysis is provided both for the curve of the matrix model with the "multi-log" potential and for the Seiberg-Witten curve in the case of SU(n) with 2n flavors, leading to the matching of the mass parameters. The isomorphism of the two curves is made manifest.Comment: 37 pages; v2: version to appear in Prog. Theor. Phys. Title changed. Isomorphism of the SU(n) spectral curve and the SW curve of Witten-Gaiotto form as well as the matching of the mass parameters more fully give

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“…If g s → 0 while keepingα i finite, the external vertex operators carry very large momenta α i = (1/g s )α i 7. It is known that[70] when b E = 1, the g s -expansion contains odd powers in g s .…”

mentioning

confidence: 99%

Method of generating q-expansion coefficients for conformal block and N=2 Nekrasov function by β-deformed matrix model

Itoyama

Oota

2010

Nuclear Physics B

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We observe that, at β-deformed matrix models for the four-point conformal block, the point q = 0 is the point where the three-Penner type model becomes a pair of decoupled two-Penner type models and where, in the planar limit, (an array of) two-cut eigenvalue distribution(s) coalesce into (that of) one-cut one(s). We treat the Dotsenko-Fateev multiple integral, with their paths under the recent discussion, as perturbed double-Selberg matrix model (at q = 0, it becomes a pair of Selberg integrals) to construct two kinds of generating functions for the q-expansion coefficients and compute some. A formula associated with the Jack polynomial is noted. The second Nekrasov coefficient for SU(2) with N f = 4 is derived. A pair of Young diagrams appears naturally. The finite N loop equation at q = 0 as well as its planar limit is solved exactly, providing a useful tool to evaluate the coefficients as those of the resolvents.The planar free energy in the q-expansion is computed to the lowest non-trivial order. A free field representation of the Nekrasov function is given. *

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Loops and unoriented strings

Cited by 7 publications

References 30 publications

Five-Dimensional AGT Relation and the Deformed -Ensemble

Five-Dimensional AGT Relation and the Deformed -Ensemble

The Quiver Matrix Model and 2d-4d Conformal Connection

Method of generating q-expansion coefficients for conformal block and N=2 Nekrasov function by β-deformed matrix model

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