# A rigorous geometric derivation of the chiral anomaly in curved backgrounds

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
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@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