1508.05345v1.pdf (1.25 MB)
A rigorous geometric derivation of the chiral anomaly in curved backgrounds
journal contribution
posted on 2016-01-14, 14:00 authored by Christian Baer, Alexander StrohmaierWe discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the $\eta$-invariant of the Cauchy hypersurfaces.
History
School
- Science
Department
- Mathematical Sciences
Citation
BAER, C. and STROHMAIER, A., 2015. A rigorous geometric derivation of the chiral anomaly in curved backgrounds. arXiv:1508.05345v1 [math-ph], 15pp.Publisher
arXiv.orgVersion
- SMUR (Submitted Manuscript Under Review)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2015Notes
This is a preprint submitted to arXiv on 21 August 2015Publisher version
Language
- en