Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems

By R. Dijkgraaf, C. Vafa. 2009

274 citations recorded by the source corpus.

We consider the topological string partition function, including the Nekrasov deformation, for type IIB geometries with an A_{n-1} singularity over a Riemann surface. These models realize the N=2 SU(n) superconformal gauge systems recently studied by Gaiotto and collaborators. Employing large N dualities we show why the partition function of topological strings in these backgrounds is captured by the chiral blocks of A_{n-1} Toda systems and derive the dictionary recently proposed by Alday, Gaiotto and Tachikawa. For the case of genus zero Riemann surfaces, we show how these systems can also be realized by Penner-like matrix models with logarithmic potentials. The Seiberg-Witten curve can be understood as the spectral curve of these matrix models which arises holographically at large N. In this context the Nekrasov deformation maps to the beta-ensemble of generalized matrix models, that in turn maps to the Toda system with general background charge. We also point out the notion of a double holography for this system, when both n and N are large.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bfe61c9887fdcc308584c3464426907f03463203

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Citations in the corpus

Quantum geometry of refined topological strings (2011, methodology): “However it is natural to extend the methods of section 4 to the β-deformed Toda matrix model [2], and show that the same result follows.”
Hitchin systems, N = 2 gauge theories and W-gravity (2009, methodology): “A derivation of the Toda/gauge correspondence has been rece tly proposed in [9] in the mirror B-model framework.”
A& B model approaches to surface operators and Toda thoeries (2010, methodology): “This is perfectly consistent with the fact that, as mentioned in section 2, the insertion of a degenerate operator in the 2d CFT corresponds to the insertion of a determinant in the matrix model language of [6].”
Penner type matrix model and Seiberg-Witten theory (2009, methodology): “[8], the following matrix model with a Penner like action W (M) = 3”
Nekrasov functions and exact Bohr-Sommerfeld integrals (2009, background): “The latter deformation, associated with a background of self-dual graviphoton, is a full topological partition function lifting F (0) from zero to arbitrary genus [ 15 ].”
The Ω Deformed B-model for Rigid N = 2 Theories (2011, unknown): “∏ i<j(λi − λj)(2) for the hermitian case [28].”
Knot Homology from Refined Chern-Simons Theory (2011, methodology): “e, Chern-Simons theory on the S(3) to topological string on X = O(−1)⊕O(−1) → IP(1)is expected to extend to the refined topological string [21,12,28].”