’t Hooft Anomalies of Discrete Gauge Theories and Non-abelian Group Cohomology
Copyright policy )’t Hooft Anomalies of Discrete Gauge Theories and Non-abelian Group Cohomology
We study discrete symmetries of Dijkgraaf-Witten theories and their gauging in the framework of (extended) functorial quantum field theory. Non-abelian group cohomology is used to describe discrete symmetries and we derive concrete conditions for such a symmetry to admit 't Hooft anomalies in terms of the Lyndon-Hochschild-Serre spectral sequence. We give an explicit realization of a discrete gauge theory with 't Hooft anomaly as a state on the boundary of a higher-dimensional Dijkgraaf-Witten theory. This allows us to calculate the 2-cocycle twisting the projective representation of physical symmetries via transgression. We present a general discussion of the bulk-boundary correspondence at the level of partition functions and state spaces, which we make explicit for discrete gauge theories.
46 pages, 1 figure; v2: minor corrections and clarifying comments added, references updated; Final version to appear in Communications in Mathematical Physics
- Heriot-Watt University
- Maxwell Institute for Mathematical Sciences United Kingdom
- Heriot-Watt University United Kingdom
High Energy Physics - Theory, Eta-invariants, Chern-Simons invariants, Strongly Correlated Electrons (cond-mat.str-el), FOS: Physical sciences, String and superstring theories in gravitational theory, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Mathematical Physics (math-ph), Anomalies in quantum field theory, Yang-Mills and other gauge theories in quantum field theory, Finite-dimensional groups and algebras motivated by physics and their representations, Spectral sequences, hypercohomology, Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Theory (hep-th), Mathematics - Quantum Algebra, FOS: Mathematics, Algebraic Topology (math.AT), Quantum Algebra (math.QA), Mathematics - Algebraic Topology, Topological field theories in quantum mechanics, Projective representations and multipliers, Cohomology theory for linear algebraic groups, Applications of global differential geometry to the sciences, Mathematical Physics
High Energy Physics - Theory, Eta-invariants, Chern-Simons invariants, Strongly Correlated Electrons (cond-mat.str-el), FOS: Physical sciences, String and superstring theories in gravitational theory, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Mathematical Physics (math-ph), Anomalies in quantum field theory, Yang-Mills and other gauge theories in quantum field theory, Finite-dimensional groups and algebras motivated by physics and their representations, Spectral sequences, hypercohomology, Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Theory (hep-th), Mathematics - Quantum Algebra, FOS: Mathematics, Algebraic Topology (math.AT), Quantum Algebra (math.QA), Mathematics - Algebraic Topology, Topological field theories in quantum mechanics, Projective representations and multipliers, Cohomology theory for linear algebraic groups, Applications of global differential geometry to the sciences, Mathematical Physics
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