Abstract
In this paper we express some simple random tensor models in a Givental-like fashion i.e. as differential operators acting on a product of generic 1-Hermitian matrix models. Finally we derive Hirota’s equations for these tensor models. Our decomposition is a first step towards integrability of such models.
Highlights
Turned out to provide an answer to that question
In this paper we express some simple random tensor models in a Giventallike fashion i.e. as differential operators acting on a product of generic 1-Hermitian matrix models
From the start tensor models were related to the group field theory (GFT) approach to quantum gravity [21, 41, 43]
Summary
For pedagogical reasons I present some known results about matrix models this should allow readers coming from different communities to read this paper . The free energy F = ln Z expands as F = g≥0 N 2−2gFg(t4) where the. The Cg coincide with the correlations functions of Liouville gravity This corresponds to the continuum limit of matrix models. One can understand that F (x) should satisfy some differential equations, that is, the differential equation satisfied by the Liouville partition function. This equation is of the Painleve type. Orthogonal polynomials allows to compute exactly the partition function of matrix model. This can be used to solve matrix models because the orthogonality relations determine completely the model. One derives recursion relations for the KN (for instance see [8] for a general description of these problems)
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