Matrix description of M-theory on T4 and T5

We study the Matrix theory description of M-theory compactified on T4 and T5. M-theory on T4 is described by the six dimensional (2,0) fixed point field theory compactified on a five torus, T5. For M-theory on T5 we suggest the existence of a new theory which is compactified on a T5. 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.