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

TL;DR

This paper explores the M(atrix) theory description of heterotic strings with Wilson lines, revealing how T-duality manifests as S-duality within the framework and detailing anomaly cancellation and fermion localization.

Contribution

It formulates a novel M(atrix) gauge theory for heterotic strings with Wilson lines, incorporating anomaly cancellation, fermion localization, and the realization of T-duality as S-duality.

Findings

Fermions are localized on orbifold boundaries or interior depending on Wilson line.

The M(atrix) theory action is uniquely fixed by anomaly cancellation.

Heterotic T-duality corresponds to electric-magnetic S-duality in 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.