M-theory of matrix models

Small M-theories incorporate various models representing a unified family in the same way that the M-theory incorporates a variety of superstring models. We consider this idea applied to the family of eigenvalue matrix models: their M-theory unifies various branches of the Hermitian matrix model (including the Dijkgraaf-Vafa partition functions) with the Kontsevich τ-function. Moreover, the corresponding duality relations are reminiscent of instanton and meron decompositions, familiar from the Yang-Mills theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 179–192, February, 2007.