$M$-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 $\tau$-function. Moreover, the corresponding duality relations are reminiscent of instanton and meron decompositions, familiar from the Yang–Mills theory.