Instantons and merons in matrix models

Various branches of matrix model partition functions 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 the 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 singularities on spectral Riemann surfaces. This construction is nothing but M -theory-like unification of various matrix models with explicit and representative realization of dualities.