Strings and matrix models on genus g Riemann Surfaces

TL;DR

This paper explores the relationships between discrete area-preserving diffeomorphisms, reduced SU(N) Yang-Mills, string theory, and the quantum Hall effect on higher-genus Riemann surfaces, highlighting connections relevant to matrix models.

Contribution

It revisits and summarizes previous work linking these mathematical and physical concepts, emphasizing their relevance to current research in matrix models.

Findings

Connections between diffeomorphisms and Yang-Mills are clarified.

Implications for string theory and quantum Hall effect are discussed.

Relevance to matrix models is highlighted.

Abstract

This is a summary of old work on connections between discrete area preserving diffeomorphisms, reduced SU(N) Yang-Mills, strings, and the quantum Hall effect on a Riemann surface of genus g. It is submitted to the archives due to the interest expressed by colleagues who are currently working on matrix models, and who could not have access to the proceedings in which the article was published. The text that follows is the version published in 1991.