The anomaly line bundle of the self-dual field theory

Abstract

In this work, we determine explicitly the anomaly line bundle of the abelian self-dual field theory over the space of metrics modulo diffeomorphisms, including its torsion part. Inspired by the work of Belov and Moore, we propose a non-covariant action principle for a pair of Euclidean self-dual fields on a generic oriented Riemannian manifold. The corresponding path integral allows to study the global properties of the partition function over the space of metrics modulo diffeomorphisms. We show that the anomaly bundle for a pair of self-dual fields differs from the determinant bundle of the Dirac operator coupled to chiral spinors by a flat bundle that is not trivial if the underlying manifold has middle-degree cohomology, and whose holonomies are determined explicitly. We briefly sketch the relevance of this result for the computation of the global gravitational anomaly of the self-dual field theory, that will appear in another paper.

41 pages. v2: A few typos corrected. Version accepted for publication in CMP

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Cited by in corpus (9)

• The anomaly that was not meant IIB
• The global anomaly of the self-dual field in general backgrounds
• Anomaly inflow and $p$-form gauge theories
• Geometric quantization and the metric dependence of the self-dual field theory
• Hamiltonian anomalies from extended field theories
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• Some comments on 6d global gauge anomalies
• On global anomalies in type IIB string theory
• Global anomalies and chiral p-forms