A note on a standard embedding on half-flat manifolds

Abstract

It is argued that the ten dimensional solution that corresponds to the compactification of E8 × E8 heterotic string theory on half-flat manifolds is the product space-time 1,2 × 7 where 7 is a generalized cylinder with G2 holonomy. Standard embedding on 7 then implies an embedding on the half-flat manifold which involves the torsionful connection rather than the Levi-Civita connection. This leads to the breakdown of E8 × E8 to E6 × E8, as in the case of the standard embedding on Calabi-Yau manifolds, which agrees with the result derived recently by Gurrieri, Lukas and Micu [1] using a different approach. Green-Schwarz anomaly cancellation is then implemented via the torsionful connection on half-flat manifolds.