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

Abstract

We study the M(atrix) theory which describes the $E_8\times E_8$ heterotic string compactified on $S^1$, or equivalently M-theory compactified on an orbifold $(S^1/\integer_2) \times S^1$, in the presence of a Wilson line. We formulate the corresponding M(atrix) gauge theory, which lives on a dual orbifold $S^1 \times (S^1 / \integer_2)$. Thirty-two real chiral fermions must be introduced to cancel gauge anomalies. In the absence of an $E_8\times E_8$ 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 IIA supergravity background into M(atrix) theory by explicitly breaking (2+1)-dimensional Poincare 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.

Latex, 39 pages, 2 figures, part of subsection 3.3 corrected

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• M(atrix) Theory on T5/Z2 Orbifold and Five-Branes
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• On Second-Quantized Open Superstring Theory
• Heterotic Matrix String Theory and Riemann Surfaces
• Superstrings from Supergravity
• Heterotic Matrix theory with Wilson lines on the lightlike circle
• Matrix Compactification On Orientifolds
• Orientifolds of Matrix theory and Noncommutative Geometry
• Elliptic Genus, Anomaly Cancellation and Heterotic M-theory
• (Supersymmetric) Kac-Moody Gauge Fields in 3+1 Dimensions
• On Heterotic/Type I Duality in d=8
• Heterotic M2-branes