Bosonic Topological Insulators and Paramagnets: a view from cobordisms

Abstract

We classify Bosonic Topological Insulators and Paramagnets in D<=4 spatial dimensions using the cobordism approach. For D<4 we confirm that the only such phase which does not fit into the group cohomology classification is the 3D Bosonic Topological Insulator protected by time-reversal symmetry whose surface admits an all-fermion topologically ordered state. For D=4 there is a unique "beyond group cohomology" phase. It is protected by gravitational anomalies of the boundary theory and is stable without any additional symmetry.

18 pages, latex. v2: an error in the last section has been corrected, affecting the classification in D=4. Other results unchanged

References in corpus (3)

• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Anomalies of discrete symmetries in various dimensions and group cohomology
• Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations

Cited by in corpus (4)

• Short-range entanglement and invertible field theories
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Homotopy Theoretic Classification of Symmetry Protected Phases
• Solvable lattice model for (2+1)D bosonic topological insulator