The uses of the refined matrix model recursion

Abstract

We study matrix models in the beta ensemble by building on the refined recursion relation proposed by Chekhov and Eynard. We present explicit results for the first beta-deformed corrections in the one-cut and the two-cut cases, as well as two applications to supersymmetric gauge theories: the calculation of superpotentials in N=1 gauge theories, and the calculation of vevs of surface operators in superconformal N=2 theories and their Liouville duals. Finally, we study the beta deformation of the Chern-Simons matrix model. Our results indicate that this model does not provide an appropriate description of the Omega-deformed topological string on the resolved conifold, and therefore that the beta-deformation might provide a different generalization of topological string theory in toric Calabi-Yau backgrounds.

29 pages, 2 figures; v2: minor changes, references added; v3: few misprints fixed, to appear on JMP; v4: we correct a mistake in Eq. (2.60) (now (2.63))

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Cited by in corpus (33)

• Quantum Geometry of Refined Topological Strings
• The Omega deformed B-model for rigid N=2 theories
• Proving AGT conjecture as HS duality: extension to five dimensions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Vertices, Vortices & Interacting Surface Operators
• Towards a proof of AGT conjecture by methods of matrix models
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Moments of the Gaussian $\beta$ Ensembles and the large-$N$ expansion of the densities
• A slow review of the AGT correspondence
• Large $N$ expansions for the Laguerre and Jacobi $\beta$ ensembles from the loop equations
• WKB Method and Quantum Periods beyond Genus One
• Quantum curves and conformal field theory
• Multiplicity-free $U_q(s{l}_N)$ 6-j symbols: relations, asymptotics, symmetries
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Loop Equation Analysis of the Circular $\beta$ Ensembles
• The classical $\beta$-ensembles with $\beta$ proportional to $1/N$: from loop equations to Dyson's disordered chain
• ABCD of Beta Ensembles and Topological Strings
• Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit
• Quantum curves from refined topological recursion: the genus 0 case
• q-holonomic formulas for colored HOMFLY polynomials of 2-bridge links
• Genus one correction to Seiberg-Witten prepotential from β-deformed matrix model
• BPS states, crystals and matrices
• Dijkgraaf-Vafa conjecture and beta-deformed matrix models
• Five-dimensional gauge theories and the local B-model
• One-cut solution of the $\beta$-ensembles in the Zhukovsky variable
• Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
• Deformation and quantisation condition of the $\mathcal{Q}$-top recursion
• Refined topological recursion revisited -- properties and conjectures
• Elements of proof for conjectures of Witte and Forrester about the combinatorial structure of Gaussian Beta Ensembles
• Loop equations for generalised eigenvalue models
• Generalized Penner model and the Gaussian beta ensemble
• $\beta$-ensembles and higher genera Catalan numbers