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 ∞-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.

Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors / Fiorenza, Domenico; Valentino, Alessandro. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 338:3(2015), pp. 1043-1074. [10.1007/s00220-015-2371-3]

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

FIORENZA, DOMENICO;
2015

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 ∞-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.
Mathematical physics
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Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors / Fiorenza, Domenico; Valentino, Alessandro. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 338:3(2015), pp. 1043-1074. [10.1007/s00220-015-2371-3]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/796578
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