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Type: Journal article
Title: The chiral anomaly of the free fermion in functorial field theory
Author: Ludewig, M.
Roos, S.
Citation: Annales Henri Poincare, 2020; 21(4):1191-1233
Publisher: Springer Nature
Issue Date: 2020
ISSN: 1424-0637
Statement of
Matthias Ludewig and Saskia Roos
Abstract: When trying to cast the free fermion in the framework of functorial field theory, its chiral anomaly manifests in the fact that it assigns the determinant of the Dirac operator to a top-dimensional closed spin manifold, which is not a number as expected, but an element of a complex line. In functorial field theory language, this means that the theory is twisted, which gives rise to an anomaly theory. In this paper, we give a detailed construction of this anomaly theory, as a functor that sends manifolds to infinite-dimensional Clifford algebras and bordisms to bimodules.
Rights: © 2020 The Author(s) Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
RMID: 1000014782
DOI: 10.1007/s00023-020-00893-6
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Appears in Collections:Mathematical Sciences publications

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