On the Moduli Spaces of M(atrix)-Theory Compactifications

TL;DR

This paper constructs the M(atrix)-Theory moduli spaces for various toroidal compactifications, revealing how BPS charges and dualities are represented and highlighting unresolved issues at higher dimensions.

Contribution

It provides a detailed M(atrix)-Theory description of Type IIA moduli spaces, including the role of theta terms and BPS charges up to n=5, and discusses challenges at n=6.

Findings

BPS charges transform under U-duality groups for n≤3

Inclusion of wrapped M-theory 5-brane charges extends the correspondence to n=4,5

Additional charges at n=6 lack clear M(atrix)-Theory candidates

Abstract

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 T^n. 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.