Leonid Chekhov

Matrix eigenvalue model: Feynman graph technique for all genera

We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power β by the Vandermonde determinant) to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint intervals (curves).

Hermitian matrix model free energy: Feynman graph technique for all genera

We present the diagrammatic technique for calculating the free energy of the Hermitian one-matrix model to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint intervals (curves).

Matrix models vs. Seiberg–Witten/Whitham theories

We discuss the relation between matrix models and the Seiberg--Witten type (SW) theories, recently proposed by Dijkgraaf and Vafa. In particular, we prove that the partition function of the Hermitean one-matrix model in the planar (large

Quantum Teichmuller space

N

Free energy topological expansion for the 2-matrix model

) limit coincides with the prepotential of the corresponding SW theory. This partition function is the logarithm of a Whitham

DV and WDVV

\tau

Topological expansion of the β-ensemble model and quantum algebraic geometry in the sectorwise approach

-function. The corresponding Whitham hierarchy is explicitly constructed. The double-point problem is solved.

Higher genus correlators from the hermitian one-matrix model

We explicitly describe a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces with holes that is equivariant with respect to the action of the mapping class group.

A Hint on the External Field Problem for Matrix Models

We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/N expansion of the nonmixed correlation functions and give a new formulation of the spectral curve. We extend these rules obtaining a closed formula for correlation functions in all orders of topological expansion. We then integrate it to obtain the free energy in terms of residues on the associated Riemann surface.

Observables in 3d gravity and geodesic algebras

We prove that the quasiclassical tau-function of the multi-support solutions to matrix models, proposed recently by Dijkgraaf and Vafa to be related to the Cachazo-Intrilligator-Vafa superpotentials of the N=1 supersymmetric Yang-Mills theories, satisfies the Witten-Dijkgraaf-Verlinde-Verlinde equations.Abstract We prove that the quasiclassical tau-function of the multi-support solutions to matrix models, proposed recently by Dijkgraaf and Vafa to be related to the Cachazo–Intrilligator–Vafa superpotentials of the N =1 supersymmetric Yang–Mills theories, satisfies the Witten–Dijkgraaf–Verlinde–Verlinde equations.