M(atrix) Theory on T5/Z2 Orbifold and Five-Branes

TL;DR

This paper explores the M(atrix) theory description of M theory on T5/Z2 orbifold, revealing how five-branes and anomalies are incorporated, and matching the resulting spectrum with (2,0) supergravity.

Contribution

It introduces a detailed M(atrix) theory framework for T5/Z2 orbifold compactification, including anomaly cancellation and five-brane dynamics.

Findings

M(atrix) theory describes M theory on T5/Z2 with USp(2N) quantum mechanics.

Anomalous G-flux at orbifold fixed points is canceled by five-branes in twisted sectors.

The derived spectrum matches (2,0) supergravity spectrum.

Abstract

We study M(atrix) theory description of M theory compactified on T5/Z2 orbifold. In the large volume limit we show that M theory dynamics is described by N=8 supersymmetric USp(2N) M(atrix) quantum mechanics. Via zero-brane parton scattering, we show that each orbifold fixed point carries anomalous G-flux $\oint [G/2 \pi]= - 1/2$. To cancel the anomalous G-flux, we introduce twisted sector consisting of sixteen five-branes represented by fundamental representation hypermultiplets. In the small volume limit we show that M theory dynamics is described by by (5+1)-dimensional (8,0) supersymmetric USp(2N) chiral gauge theory. We point out that both perturbative and global gauge anomalies are cancelled by the sixteen fundamental representation hyper- multiplets in the twisted sector. We show that M(atrix) theory is capable of turning on spacetime background with the required sixteen five-branes out of zero-brane partons as bound-states. We determine six-dimensional spacetime spectrum from the M(atrix) theory for both untwisted and twisted sectors and find a complete agreement with the spectrum of (2,0) supergravity. We discuss M(atrix) theory description of compactification moduli space, symmetry enhance- ment thereof as well as further toroidal compactifications.