On the Duality between Perturbative Heterotic Orbifolds and M-Theory on T^4/Z_N

TL;DR

This paper explores the duality between heterotic orbifold compactifications and M-theory, proposing a resolution for the distribution of matter multiplets and analyzing gauge coupling and anomaly cancellation.

Contribution

It introduces a novel scenario for localizing matter multiplets on boundary planes in M-theory duals of heterotic orbifolds, resolving a key paradox.

Findings

Evidence for gauge group mixing on connecting seven-planes

Verification of local anomaly cancellation

Analysis of gauge couplings in the dual setup

Abstract

The heterotic $E_8\times E_8$ string compactified on an orbifold $T^4/\IZ_N$ has gauge group $G\times G'$ with (massless) states in its twisted sectors which are charged under both gauge group factors. In the dual M-theory on $(T^4/\IZ_N)\otimes(S^1/\IZ_2)$ the two group factors are separated in the eleventh direction and the G and G' gauge fields are confined to the two boundary planes, respectively. We present a scenario which allows for a resolution of this apparent paradox and assigns all massless matter multiplets locally to the different six-dimensional boundary fixed planes. The resolution consists of diagonal mixing between the gauge groups which live on the connecting seven-planes (6d and the eleventh dimension) and one of the gauge group factors. We present evidence supporting this mixing by considering gauge couplings and verify local anomaly cancellation. We also discuss open problems which arise in the presence of U_1 factors.