The Hitchin Functionals and the Topological B-Model at One Loop |
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Authors: | Email author" target="_blank">Vasily?PestunEmail author Edward?Witten |
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Institution: | (1) Physics Department Jadwin Hall, Princeton University, Princeton, NJ 08544, USA;(2) Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA;(3) ITEP, 117259 Moscow, Russia |
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Abstract: | 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 Kähler metrics |
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Keywords: | generalized complex structures topological M-theory topological B-model |
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