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A rigorous geometric derivation of the chiral anomaly in curved backgrounds

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journal contribution
posted on 2016-04-19, 09:52 authored by Christian Baer, Alexander Strohmaier
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 directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the η-invariant of the Cauchy hypersurfaces.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Communications in Mathematical Physics

Volume

347

Issue

3

Pages

703 - 721

Citation

BAER, C. and STROHMAIER, A., 2016. A rigorous geometric derivation of the chiral anomaly in curved backgrounds. Communications in Mathematical Physics, 347 (3), pp. 703-721.

Publisher

© Springer Verlag (Germany)

Version

  • AM (Accepted Manuscript)

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/

Acceptance date

2016-03-30

Publication date

2016-05-27

Notes

The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-016-2664-1.

ISSN

0010-3616

eISSN

1432-0916

Language

  • en

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