Abstract
AbstractWhen 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.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
Reference23 articles.
1. Atiyah, M.: Topological quantum field theories. Inst. Hautes Études Sci. Publ. Math. 68(1989), 175–186 (1988)
2. Atiyah, M.F., Patodi, V.K., Singer, I.M.: Spectral asymmetry and Riemannian geometry. I. Math. Proc. Camb. Philos. Soc. 77, 43–69 (1975)
3. Ayala, D.: Geometric Cobordism Categories. ProQuest LLC, Ann Arbor, MI, 2009. Thesis (Ph.D.)—Stanford University
4. Bär, C.: On nodal sets for Dirac and Laplace operators. Commun. Math. Phys. 188(3), 709–721 (1997)
5. Berline, N., Getzler, E., Vergne, M.: Heat Kernels and Dirac Operators, Volume 298 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Berlin (1992)
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