Orbifold and Five-branes

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 ∮ [G/2π] = −1/2. To cancel the anomalous Gflux , 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 effectively 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 hypermultiplets in the twisted sector. We show that M(atrix) theory is capable of turning on spacetime background with the required sixteen fivebranes 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 enhancement thereof as well as further toroidal compactifications. 1 Work supported in part by the NSF-KOSEF Bilateral Grant, KOSEF Purpose-Oriented Research Grant 94-1400-04-01-3 and SRC-Program, Ministry of Education Grant BSRI 97-2418, the Monell Foundation and the Seoam Foundation Fellowships, SNU Research Fund, and the Korea Foundation for Advanced Studies Faculty Fellowship.