The Hitchin Functionals and the Topological B-Model at One Loop

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 Kahler metrics. * On leave of absense from ITEP, 117259, Moscow, Russia 7 When the cohomology groups are nonzero, they contribute to Z HE an additional factor

Hitchin functionals are related to measures of entanglement

“…It turned out 44 that in order to achieve agreement at one loop level one has to use the an entanglement measure for a fermionic system with six single particle states with either an even or add number of particles. An alternative interpretation can also be given in terms of the tripartite entanglement of six qubits a structure living naturally inside the recently discovered tripartite entanglement of seven qubits 9,10,21 .…”

Link invariants for flows in higher dimensions

“…Moreover, the Hitchin functional M 7 Φ ∧ ⋆ 7 Φ is defined on a 7 manifold M 7 of G 2 -holonomy, which resembles a BF action. It is worth to mention that the partition function at one-loop has been computed recently [41,42] in terms of the BV formalism by obtaining the Ray-Singer torsion of M 7 . It would be interesting to find the observables of the theory and their asymptotic counterparts.…”

Topological strings in generalized complex space

“…There is a dependence of the partition function on the base point, since the base point defines the measure in the BV path integral. It is possible that a background independent model could be formulated along the lines of [11,16,35,[80][81][82]. 11 In their construction, the authors start from eight fields instead of six.…”

“…In a spirit similar to [82], one can also compute the 1-loop partition function in (3.53) and find a certain product of generalized Ray-Singer torsions in terms of determinants of generalized∂ L , ∂ L operators of the Lie algebroid [118].…”