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

TL;DR

This work proposes a nonperturbative definition of heterotic M(atrix) theory in the presence of a Wilson line by formulating a 2+1D gauge theory on a dual orbifold and enforcing gauge and supersymmetry anomaly cancellation. The resulting action features position-dependent Yang-Mills and Chern-Simons couplings that encode background fields from D8-branes, explicitly breaking 2+1D Poincaré invariance to incorporate the massive IIA background. The authors identify BPS spectra in both untwisted and twisted sectors and show precise matches to heterotic string states, uncovering a novel electric-magnetic S-duality in 2+1D that realizes heterotic T-duality. This links heterotic moduli and Wilson-line deformations to D-brane backgrounds within M(atrix) theory and suggests that non-Lorentz-invariant field theories can capture essential background geometries in M-theory constructions.

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.

Figures (1)

• Figure 1: Type IA and $\widetilde{\hbox{\rm IA}}$ compactifications for unbroken $E_8 \times E_8$. There are 8 D8-branes at every orientifold, giving $SO(16)$ gauge symmetry.