We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical problems.

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Intersection theory on the moduli space of curves and the matrix Airy function

R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.

Exactly Solved Models in Statistical Mechanics

Annals of physics

We study $ \mathcal{N} = 2 $ supersymmetric four-dimensional gauge theories, in a certain 525-02 = 2 supergravity background, called theΩ-background. The partition function of the theory in the Ω-background can be calculated explicitly. We investigate various representations for this partition function: a statistical sum over random partitions, a partition function of the ensemble of random curves, and a free fermion correlator.

http://math.univ-lyon1.fr/~attal/Okounkov/okounkov-nekrasov

Seiberg-Witten theory and random partitions

2D gravity and random matrices

Integrability and Seiberg-Witten exact solution

The exact Seiberg-Witten (SW) description of the light sector in the $N=2$ SUSY $4d$ Yang-Mills theory is reformulated in terms of integrable systems and appears to be a Gurevich-Pitaevsky (GP) solution to the elliptic Whitham equations. We consider this as an implication that dynamical mechanism behind the SW solution is related to integrable systems on the moduli space of instantons. We emphasize the role of the Whitham theory as a possible substitute of the renormalization-group approach to the construction of low-energy effective actions.

An. Morozov

Papers

Integrability and Seiberg-Witten exact solution

Integrability and Seiberg-Witten Exact Solution

On non-conformal limit of the AGT relations

Conformal matrix models as an alternative to conventional multi-matrix models

Integrability and Seiberg-Witten theory curves and periods