Journal
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
Volume 59, Issue 10, Pages 937-1015Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/prop.201100048
Keywords
Anomalies; gravitatinal instantons; Lifshitz gravity
Categories
Funding
- Cluster of Excellence Origin and the Structure of the Universe in Munich, Germany
Ask authors/readers for more resources
We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z = 3 which is minimally coupled to geometry in 3 + 1 space-time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the eta-invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non-relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Horava-Lifshitz theory and find that the index is non-zero provided that the space-time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2) x U(1) isometry. In contrast to the instantons of Einstein gravity, chiral symmetry breaking becomes possible in the unimodular phase of Horava-Lifshitz theory arising at lambda = 1/3 provided that the volume of space is bounded from below by the ratio of the Ricci to Cotton tensor couplings raised to the third power. Some other aspects of the anomalies in non-relativistic quantum field theories are also discussed. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available