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By Edward Witten; Peter Svrcek; Stanford Linear Accelerator Center. .; United States. Dept. of Energy.; United States. Dept. of Energy. Office of Scientific and Technical Information

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A more complicated structure of vanishing cycles might be necessary. Axion Physics With A Small S 3 In the case when X develops a vanishing S 3 , we can be more precise in estimating Fc , as the explicit metric of the local G2 holonomy manifold with vanishing S 3 is known [76]. Locally the manifold has the topology S 3 × R4 /Γ, where Γ is a finite subgroup of SU (2) with which we orbifold R4 to get nonabelian gauge symmetry. Asymptotically, the manifold is a cone over S 3 × S 3 /Γ where the S 3 is homologous to the vanishing three-cycle Q and S 3 /Γ is the quotient of the unit three-sphere in R4 .

Asymmetric Calabi-Yau Manifolds As an alternative to assuming that Q is a vanishing cycle, one can ask whether taking an asymmetric Calabi-Yau manifold that is a fibration with small fiber F over a large base B could substantially lower the axion coupling parameter. Based on our experience with heterotic string in section 3 we expect that the decay constants of axions in asymmetric compactifications are still around the GUT scale. To explore this question, we will consider supersymmetric fibrations with T 2 , T 3 or K3 fibers, but our conclusions apply to more general fibrations (including nonsupersymmetric 45 ones).

B. Green, J. H. Schwarz, and E. Witten, Superstring Theory, vol. 2 (Cambridge University Press, 1987). [31] S. Barr, “Harmless Axions In Superstring Theories,” Phys. Lett. B158 (1985) 397. [32] A. Linde, “Inflation And Axion Cosmology,” Phys. Lett. B201 (1988) 437. [33] K. Choi and J. E. Kim, “Harmful Axions In Superstring MOdels,” Phys. Lett. B154 (1985) 393, “Compactification And Axions In E8 × E8′ Superstring Models,” Phys. Lett. B165 (1985) 689. [34] P. Fox, A. Pierce, and S. Thomas, “Probing A QCD String Axion With Precision Cosmological Measurements,” hep-th/0409059.

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