M(atrix) Theory on an Orbifold and Twisted Membrane

TL;DR

This paper investigates M(atrix) theory on orbifolds, focusing on heterotic models, gauge group choices, and the resulting topologies and spectra of twisted two-branes, revealing conditions for supersymmetry and anomaly cancellation.

Contribution

It identifies possible gauge groups in heterotic M(atrix) theory and analyzes how these choices affect two-brane topologies and spectra, advancing understanding of orbifold M-theory.

Findings

Only SO(2N) and SO(2N+1) gauge groups support open two-branes.

Twisted sector spectra include sixteen fundamental spinors at each fixed point.

Supersymmetric twisted sectors satisfy anomaly and vacuum energy cancellation.

Abstract

M(atrix) theory on an orbifold and classical two-branes therein are studied with particular emphasis to heterotic M(atrix) theory on $S_1/Z_2$ relevant to strongly coupled heterotic and dual Type IA string theories. By analyzing orbifold condition on Chan-Paton factors, we show that three choice of gauge group are possible for heterotic M(atrix) theory: SO(2N), SO(2N+1) or USp(2N). By examining area-preserving diffeomorphism that underlies the M(atrix) theory, we find that each choices of gauge group restricts possible topologies of two-branes. The result suggests that only the choice of SO(2N) or SO(2N+1) groups allows open two-branes, hence, relevant to heterotic M(atrix) theory. We show that requirement of both local vacuum energy cancellation and of worldsheet anomaly cancellation of resulting heterotic string identifies supersymmetric twisted sector spectra with sixteen fundamental representation spinors from each of the two fixed points. Twisted open and closed two-brane configurations are obtained in the large N limit.