ar X iv : h ep - t h / 06 08 22 8 v 1 31 A ug 2 00 6 Instantons and Merons in Matrix Models

Various branches of matrix model partition function can be represented as intertwined products of universal elementary constituents: Gaussian partition functions Z G and Kontsevich τ-functions Z K. In physical terms, this decomposition is the matrix-model version of multi-instanton and multi-meron configurations in Yang-Mills theories. Technically, decomposition formulas are related to representation theory of algebras of Krichever-Novikov type on families of spectral curves with additional Seiberg-Witten structure. Representations of these algebras are encoded in terms of " the global partition functions ". They interpolate between Z G and Z K associated with different singu-larities on spectral Riemann surfaces. This construction is nothing but M-theory-like unification of various matrix models with explicit and representative realization of dualities.