Modular Matrix Models

TL;DR

This paper introduces a modular matrix model inspired by modular forms and matrix models, which encodes the Klein j-invariant and connects to the Monster group via Moonshine, bridging algebra, geometry, and physics.

Contribution

It constructs a novel Hermitian one-matrix model that captures modular form properties and relates to advanced algebraic structures like the Monster group.

Findings

The model encodes the Klein j-invariant.

Connections established between matrix models and Moonshine.

Links to N=1 gauge theory and Calabi-Yau geometry.

Abstract

Inspired by a formal resemblance of certain q-expansions of modular forms and the master field formalism of matrix models in terms of Cuntz operators, we construct a Hermitian one-matrix model, which we dub the ``modular matrix model.'' Together with an N=1 gauge theory and a special Calabi-Yau geometry, we find a modular matrix model that naturally encodes the Klein elliptic j-invariant, and hence, by Moonshine, the irreducible representations of the Fischer-Griess Monster group.