Instantons and Merons in Matrix Models

TL;DR

This paper explores the decomposition of matrix model partition functions into elementary components, revealing a unifying structure akin to M-theory that connects different models and dualities through algebraic and geometric frameworks.

Contribution

It introduces a novel decomposition of matrix model partition functions into universal constituents, linking algebraic representation theory with spectral curve geometry, and unifying various models within a M-theory-like framework.

Findings

Decomposition formulas relate matrix models to spectral curve algebras.

Partition functions interpolate between Gaussian and Kontsevich models.

Framework encodes dualities and unifies different matrix models.

Abstract

Various branches of matrix model partition function can be represented as intertwined products of universal elementary constituents: Gaussian partition functions Z_G and Kontsevich tau-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 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.