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

Vasily Pestun, Edward Witten

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)21-51
Number of pages31
JournalLetters in Mathematical Physics
Volume74
Issue number1
DOIs
StatePublished - Oct 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Generalized complex structures
  • Topological B-model
  • Topological M-theory

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