Matrix models of two-dimensional gravity and Toda theory

Gerasimov, A.; Marshakov, A.; Миронов, А.; Морозов, Алексей Юрьевич; Orlov, A. Yu.

doi:10.1016/0550-3213(91)90482-d

Cited by 262 publications

(323 citation statements)

References 28 publications

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“…In this section we review the exact constraints for the planar level free energy F m of the one-matrix model [18,19]. We consider the U(N ) matrix model that is related to the U(N ) gauge theory with the adjoint scalar.…”

Section: Virasoro Constraints For the One-matrix Modelmentioning

confidence: 99%

On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture

Svrcek

2004

J. High Energy Phys.

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In this paper we study the nonperturbative corrections to the generalized Konishi anomaly that come from the strong coupling dynamics of the gauge theory. We consider U (N ) gauge theory with adjoint and Sp(N ) or SO(N ) gauge theory with symmetric or antisymmetric tensor. We study the algebra of chiral rotations of the matter field and show that it does not receive nonperturbative corrections. The algebra implies Wess-Zumino consistency conditions for the generalized Konishi anomaly which are used to show that the anomaly does not receive nonperturbative corrections for superpotentials of degree less than 2l + 1 where 2l = 3c(Adj) − c(R) is the one-loop beta function coefficient. The superpotentials of higher degree can be nonperturbatively renormalized because of the ambiguities in the UV completion of the gauge theory. We discuss the implications for the Dijkgraaf-Vafa conjecture.

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Section: Virasoro Constraints For the One-matrix Modelmentioning

confidence: 99%

On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture

Svrcek

2004

J. High Energy Phys.

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“…On the level of the Toda chain hierarchy, which governs the dynamics over the parameters of the potential [29], one deals here with two completely different solutions to the Toda equation…”

Section: Eguchi-yang Matrix Modelmentioning

confidence: 99%

Gauge theories as matrix models

Marshakov

2011

Theor Math Phys

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The relation between the Seiberg-Witten prepotentials, Nekrasov functions and matrix models is discussed. The matrix models of Eguchi-Yang type are derived quasiclassically as describing the instantonic contribution to the deformed partition functions of supersymmetric gauge theories. The constructed explicitly exact solution for the case of conformal four-dimensional theory is studied in detail, and some aspects of its relation with the recently proposed logarithmic beta-ensembles are considered. We discuss also the "quantization" of this picture in terms of twodimensional conformal theory with extended symmetry, and stress its difference from common picture of perturbative expansion a la matrix models. Instead, the representation for Nekrasov functions in terms of conformal blocks or Whittaker vector suggests some nontrivial relation with Teichmüller spaces and quantum integrable systems.

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“…For n = m, we get the equation which determines the leading contribution u (1) in the double scaling limit…”

Section: Note Thatũ (0) (V) = U (0) (V) By Substituting (86)-(87) Inmentioning

confidence: 99%

“…Many exciting properties of the Hermitian matrix model emerge in its large-N limit. They can be described by taking the continuum limit [1,9] of the scheme provided by the basic equations (2) and (4). The aim of the present paper is to present an alternative way to analyze the large-N limit.…”

Section: P N (Z T)p M (Z T)e V (Zt) Dz = H N (T)δ Nm V(zt)mentioning

confidence: 99%