The Hitchin functionals and the topological B-model at one loop

Details The Hitchin functionals and the topological B-model at one loop The Hitchin functionals and the topological B-model at one loop

2005-03-09

arxiv.org/abs/hep-th/0503083v2

Lett.Math.Phys.74:21-51,2005

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, LaTeX

Scientific paper

10.1007/s11005-005-0007-9

The quantization in quadratic order of the Hitchin functional, which defines by critical points a Calabi-Yau structure on a six-dimensional manifold, is performed. The conjectured relation between the topological B-model and the Hitchin functional is studied at one loop. It is found that the genus one free energy of the topological B-model disagrees with the one-loop free energy of the minimal Hitchin functional. However, the topological B-model does agree at one-loop order with the extended Hitchin functional, which also defines by critical points a generalized Calabi-Yau structure. The dependence of the one-loop result on a background metric is studied, and a gravitational anomaly is found for both the B-model and the extended Hitchin model. The anomaly reduces to a volume-dependent factor if one computes for only Ricci-flat Kahler metrics.

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