A Note on a Standard Embedding on Half-Flat Manifolds

Details A Note on a Standard Embedding on Half-Flat Manifolds A Note on a Standard Embedding on Half-Flat Manifolds

2007-11-21

arxiv.org/abs/0711.3248v3

JHEP 0807:121,2008

Physics

High Energy Physics

High Energy Physics - Theory

5 pages. v2: 6 pages; slightly reworded; version submitted for publication. v3: uses JHEP3.cls, hence 14 pages now. Essentiall

Scientific paper

10.1088/1126-6708/2008/07/121

It is argued that the ten dimensional solution that corresponds to the compactification of $E_8 \times E_8$ heterotic string theory on a half-flat manifold is the product space-time $R^{1,2} \times Z_7$ where $Z_7$ is a generalized cylinder with $G_2$ riemannian holonomy. Standard embedding on $Z_7$ 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 $E_8 \times E_8$ to $E_6 \times E_8$, as in the case of the standard embedding on Calabi-Yau manifolds, which agrees with the result derived recently by Gurrieri, Lukas and Micu (arXiv:0709.1932) using a different approach. Green-Schwarz anomaly cancellation is then implemented via the torsionful connection on half-flat manifolds.

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