A rigorous geometric derivation of the chiral anomaly in curved backgrounds

Christian Bär, Alexander Strohmaier
August 21, 2015
We 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.
open access link Commun. Math. Phys. 347 (2016), 703-721
%%% contains utf-8, see: http://inspirehep.net/info/faq/general#utf8 %%% add \usepackage[utf8]{inputenc} to your latex preamble @article{Baer:2015tka, author = "Bär, Christian and Strohmaier, Alexander", title = "{A rigorous geometric derivation of the chiral anomaly in curved backgrounds}", journal = "Commun. Math. Phys.", volume = "347", year = "2016", number = "3", pages = "703-721", doi = "10.1007/s00220-016-2664-1", eprint = "1508.05345", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1508.05345;%%" }

Keywords: 
chiral anomaly, Lorentzian index theorem, QFT on curved spacetimes