Holomorphically Covariant Matrix Models

TL;DR

This paper introduces a method to build matrix models on any simply connected oriented Riemannian surface, ensuring invariance under holomorphic transformations of the matrix coordinates.

Contribution

It provides a novel construction of matrix models with holomorphic invariance on arbitrary 2D Riemannian manifolds.

Findings

Matrix models can be constructed on arbitrary simply connected Riemann surfaces.

The actions and measures are invariant under holomorphic transformations.

This invariance extends the applicability of matrix models in geometric contexts.

Abstract

We present a method to construct matrix models on arbitrary simply connected oriented real two dimensional Riemannian manifolds. The actions and the path integral measure are invariant under holomorphic transformations of matrix coordinates.