Matrix Description of M-theory on $T^4$ and $T^5$

TL;DR

This paper explores the Matrix theory descriptions of M-theory compactified on $T^4$ and $T^5$, proposing new theories and highlighting differences from standard super-Yang-Mills approaches.

Contribution

It introduces a novel Matrix theory framework for M-theory on $T^4$ and $T^5$, including a new non-critical string theory for the $T^5$ case.

Findings

M-theory on $T^4$ described by (2,0) theory on $ ilde T^5$

Proposal of a new non-critical string theory for M-theory on $T^5$

Differences from standard super-Yang-Mills descriptions

Abstract

We study the Matrix theory description of M-theory compactified on $T^4$ and $T^5$. M-theory on $T^4$ is described by the six dimensional (2,0) fixed point field theory compactified on a five torus, $\widetilde T^5$. For M-theory on $T^5$ we suggest the existence of a new theory which is compactified on a $\widetilde T^5$. The IR description of this theory is given by the (2,0) theory with a compactified moduli space. This new theory appears to be a new kind of a non-critical string theory. Clearly, these two descriptions differ from the ``standard'' Super-Yang-Mills on the dual torus prescription.