Andrey I. Marshakov

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We discuss the AdS/CFT duality from the perspective of integrable systems and establish a direct relationship between the dimension of single trace local operators composed of two types of scalar fields in N = 4 super YangMills and the energy of their dual semiclassical string states in AdS5 × S. The anomalous dimensions can be computed using a set of Bethe(More)
We represent the partition function of the Generalized Kontsevich Model (GKM) in the form of a Toda lattice τ -function and discuss various implications of non-vanishing ”negative”and ”zero”-time variables: the appear to modify the original GKM action by negative-power and logarithmic contributions respectively. It is shown that so deformed τ -function(More)
We introduce a new 1-matrix model with arbitrary potential and the matrix-valued background field. Its partition function is a τ -function of KPhierarchy, subjected to a kind of L−1-constraint. Moreover, partition function behaves smoothly in the limit of infinitely large matrices. If the potential is equal to X, this partition function becomes a τ(More)
We introduce conformal multi-matrix models (CMM) as an alternative to conventional multi-matrix model description of two-dimensional gravity interacting with c < 1 matter. We define CMM as solutions to (discrete) extended Virasoro constraints. We argue that the so defined alternatives of multi-matrix models represent the same universality classes in(More)
A 1-matrix model is proposed, which nicely interpolates between doublescaling continuum limits of all multimatrix models. The interpolating partition function is always a KP τ -function and always obeys L−1-constraint and string equation. Therefore this model can be considered as a natural unification of all models of 2d-gravity (string models) with c ≤ 1.(More)
We consider the deformations of “monomial solutions” to Generalized Kontsevich Model [1, 2] and establish the relation between the flows generated by these deformations with those of N = 2 Landau-Ginzburg topological theories. We prove that the partition function of a generic Generalized Kontsevich Model can be presented as a product of some(More)
The Kazakov-Migdal model, if considered as a functional of external fields, can be always represented as an expansion over characters of GL group. The integration over ”matter fields” can be interpreted as going over the model (the space of all highest weight representations) of GL. In the case of compact unitary groups the integrals should be substituted(More)