Higher Loop Effects in M(atrix) Orbifolds

TL;DR

This paper investigates higher loop effects in M(atrix) orbifolds, revealing a two-loop correction to the moduli space metric and discussing discrepancies with M(atrix) theory predictions, with implications for non-compact backgrounds.

Contribution

It explicitly calculates the two-loop correction to the moduli space metric in M(atrix) orbifolds and discusses its implications and discrepancies with M(atrix) theory.

Findings

Two-loop correction to the moduli space metric is non-zero.

No higher-loop contributions beyond two loops.

Discrepancy in N-dependence with M(atrix) theory predictions.

Abstract

Scattering of zero branes off the fixed point in $R^8/Z_2$, as described by a super-quantum mechanics with eight supercharges, displays some novel effects relevant to Matrix theory in non-compact backgrounds. The leading long distance behaviour of the moduli space metric receives no correction at one loop in Matrix theory, but does receive a correction at two loops. There are no contributions at higher loops. We explicitly calculate the two-loop term, finding a non-zero result. We find a discrepancy with M(atrix)-theory. Although the result has the right dependence on $v$ and $b$ for the scattering of zero branes off the fixed point the factors of $N$ do not match. We also discuss scattering in the orbifolds, $R^5/Z_2$ and $R^9/Z_2$ where we find the predicted fractional charges.