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A rigorous geometric derivation of the chiral anomaly in curved backgrounds

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journal contribution
posted on 2016-01-14, 14:00 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 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.org

Version

  • 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

2015

Notes

This is a preprint submitted to arXiv on 21 August 2015

Language

  • en

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