Aspects of ALE Matrix Models and Twisted Matrix Strings

TL;DR

This paper explores the formulation of M(atrix)-Theory on ALE spaces, proposing models that include massless vectors and twisted orbifold descriptions, advancing understanding of gauge symmetries and string interactions in these geometries.

Contribution

It introduces a matrix model for M-Theory on ALE spaces with wrapped membranes and classifies twisted matrix string theories via Reid's sequences.

Findings

Massless vector multiplets exist in resolved ALE spaces.

Proposed matrix model captures M-Theory with wrapped membranes.

Classified twisted matrix string theories using surface quotient singularities.

Abstract

We examine several aspects of the formulation of M(atrix)-Theory on ALE spaces. We argue for the existence of massless vector multiplets in the resolved $A_{n-1}$ spaces, as required by enhanced gauge symmetry in M-Theory, and that these states might have the correct gravitational interactions. We propose a matrix model which describes M-Theory on an ALE space in the presence of wrapped membranes. We also consider orbifold descriptions of matrix string theories, as well as more exotic orbifolds of these models, and present a classification of twisted matrix string theories according to Reid's exact sequences of surface quotient singularities.