The Hopf invariants of 3D topological insulators are identified with Dixmier-Douady invariants of tensor Berry connections, which quantize magnetoelectric and shift-current responses.
Quantization of Higher Abelian Gauge Theory in Generalized Differential Cohomology
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We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons cohomology, and of Ramond-Ramond fields in Type II superstring theory and differential K-theory.
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Probing Tensor Monopoles and Gerbe Invariants in Three-Dimensional Topological Matter
The Hopf invariants of 3D topological insulators are identified with Dixmier-Douady invariants of tensor Berry connections, which quantize magnetoelectric and shift-current responses.