Wilson Lines and T - Duality in Heterotic M ( atrix ) Theory

We study the M(atrix) theory which describes the E8×E8 heterotic string compactified on S , or equivalently M-theory compactified on an orbifold (S/Z 2)×S, in the presence of a Wilson line. We formulate the corresponding M(atrix) gauge theory, which lives on a dual orbifold S × (S/Z 2). Thirty-two real chiral fermions must be introduced to cancel gauge anomalies. In the absence of an E8 × E8 Wilson line, these fermions are symmetrically localized on the orbifold boundaries. Turning on the Wilson line moves these fermions into the interior of the orbifold. The M(atrix) theory action is uniquely determined by gauge and supersymmetry anomaly cancellation in 2+1 dimensions. The action consistently incorporates the massive I IA supergravity background into M(atrix) theory by explicitly breaking (2+1)-dimensional Poincaré invariance. The BPS excitations of M(atrix) theory are identified and compared to the heterotic string. We find that heterotic T-duality is realized as electric-magnetic S-duality in M(atrix) theory. 1 Work supported in part by NSF grant NSF-PHY-9318781, the NSF-KOSEF Bilateral Grant, KOSEF Purpose-Oriented Research Grant 94-1400-04-01-3 and SRC-Program, Ministry of Education Grant BSRI 972410, the Monell Foundation and the Seoam Foundation Fellowships.