On the moduli spaces of M(atrix)-theory compactifications

By identifying the moduli space of coupling constants in the SYM description of toroidal compactifications of M(atrix)-theory, we construct the M(atrix) description of the moduli spaces of type IIA string theory compactified on Tⁿ. Addition of theta terms to the M(atrix) SYM produces the shift symmetries necessary to recover the correct global structure of the moduli spaces. Up to n = 3, the corresponding BPS charges transform under the proper representations of the U-duality groups. For n = 4, 5, if we make the ansatz of including the BPS charges corresponding to the wrapped M-theory 5-brane, the correspondence with type IIA continues to hold. However, for n = 6, we find additional charges for which there are no obvious candidates in M(atrix)-theory.