Michael B. Schulz, Elliott F. Tammaro
We review the geometry of K3 surfaces and then describe this geometry from the point of view of an approximate metric of Gibbons-Hawking form. This metric arises from the M-theory lift of the tree-level supergravity description of type IIA string theory on the T^3/Z_2 orientifold, the D6/O6 orientifold T-dual to type I on T^3. At large base, it provides a good approximation to the exact K3 metric everywhere except in regions that can be made arbitrarily small. The metric is hyperk\"ahler, and we give explicit expressions for the hyperk\"ahler forms as well as harmonic representatives of all cohomology classes. Finally we compute the metric on the moduli space of approximate metrics in two ways, first by projecting to transverse traceless deformations (using compensators), and then by computing the naive moduli space metric from dimensional reduction. In either case, we find agreement with the exact coset moduli space of K3 metrics. The T^3/Z_2 orientifold provides a simple example of a warped compactification. In a companion paper, the results of this paper will be applied to study the procedure for warped Kaluza-Klein reduction on T^3/Z_2.
View original:
http://arxiv.org/abs/1206.1070
No comments:
Post a Comment