Non-Orientable M(atrix) Theory

TL;DR

This paper explores M(atrix) theory formulations for M-theory compactified on non-orientable manifolds, revealing new gauge theories and spectra consistent with M-theory predictions.

Contribution

It introduces M(atrix) theory descriptions for non-orientable compactifications, including Klein bottle, M"obius strip, and CHL models, with detailed gauge theory and spectrum analysis.

Findings

M(atrix) theory on Klein bottle and M"obius strip yields (2+1)-D supersymmetric gauge theories.

A twisted sector with chiral fermions is necessary for M"obius strip compactification.

Low-energy dynamics of CHL compactification is described by (5+1)-D gauge theory matching M-theory results.

Abstract

M(atrix) theory description is investigated for M-theory compactified on non-orientable manifolds. Relevant M(atrix) theory is obtained by Fourier transformation in a way consistent with T-duality. For nine-dimensional compactification on Klein bottle and M\"obius strip, we show that M(atrix) theory is (2+1)-dimensional ${\cal N} = 8$ supersymmetric U(N) gauge theory defined on dual Klein bottle and dual Moebius strip parameter space respectively. The latter requires a twisted sector consisting of sixteen chiral fermions localized parallel to the boundary of dual Moebius strip and defines Narain moduli space of Chaudhuri-Hockney-Lykken heterotic string. For six-dimensional CHL compactification on S1/Z2*T4 we show that low-energy dynamics of M(atrix) theory is described by (5+1)-dimensional ${\cal N} = 8$ supersymmetric U(N)$\times$U(N) gauge theory defined on dual orbifold parameter space of S1*K3/Z2. Spacetime spectrum is deduced from BPS gauge field configurations consistent with respective involutions and is shown to agree with results from M-theory analysis.