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arXiv · 1409.5723

Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors

Domenico Fiorenza·Alessandro Valentino
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Abstract

We study boundary conditions for extended topological quantum field theories (TQFTs) and their relation to topological anomalies. We introduce the notion of TQFTs with moduli level $m$, and describe extended anomalous theories as natural transformations of invertible field theories of this type. We show how in such a framework anomalous theories give rise naturally to homotopy fixed points for $n$-characters on $\infty$-groups. By using dimensional reduction on manifolds with boundaries, we show how boundary conditions for $n+1$-dimensional TQFTs produce $n$-dimensional anomalous field theories. Finally, we analyse the case of fully extended TQFTs, and show that any fully extended anomalous theory produces a suitable boundary condition for the anomaly field theory.

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Domenico Fiorenza, Alessandro Valentino. 2015-01-22. Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors. https://doi.org/10.1007/s00220-015-2371-3

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