M ( atrix ) Theory on T 5 / Z 2 Orbifold and Five - Branes 1

We show that compactification of the M(atrix) theory on orbifold T5/Z2 is described by N = 8 supersymmetric quantum mechanics with USp(2N) gauge group and Spin(5)⊗Spin(4) R-symmetry. Using zero-brane and two-brane as probes, we find that each of the thirtytwo orbifold fixed points carry G-flux ∮ [G/2π] = −1/2. This anomalous G-flux is cancelled supersymmetrically by turning on sixteen longitudinal five-branes on six-dimensional spacetime. We determine six-dimensional spacetime spectrum from the M(atrix) theory for both untwisted and twisted sectors and find a complete agreement with known results that are determined from low-energy supergravity and anomaly cancellation analysis. We discuss moduli space and symmetry enhancement thereof in M(atrix) theory as well as duality relations to type IIB string on K3 and to heterotic and type I strings on T4. Submitted to Nuclear Physics B 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 97-2410, the Monell Foundation and the Seoam Foundation Fellowships.