Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect

Abstract

We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not possess topological order and are bosonic analogs of free fermion topological insulators and superconductors. While a formal cohomology based classification of such states was recently discovered, their physical properties remain mysterious. Here we develop a field theoretic description of several of these states and show that they possess unusual surface states, which if gapped, must either break the underlying symmetry, or develop topological order. In the latter case, symmetries are implemented in a way that is forbidden in a strictly two dimensional theory. While this is the usual fate of the surface states, exotic gapless states can also be realized. For example, tuning parameters can naturally lead to a deconfined quantum critical point or, in other situations, a fully symmetric vortex metal phase. We discuss cases where the topological phases are characterized by quantized magnetoelectric response θ, which, somewhat surprisingly, is an odd multiple of 2π. Two different surface theories are shown to capture these phenomena - the first is a nonlinear sigma model with a topological term. The second invokes vortices on the surface that transform under a projective representation of the symmetry group. A bulk field theory consistent with these properties is identified, which is a multicomponent `BF' theory supplemented, crucially, with a topological term. A possible topological phase characterized by the thermal analog of the magnetoelectric effect is also discussed.

25 pages+ 3 pages Appendices, 3 figures. Introduction rewritten for clarity, minor technical changes and additional details of surface topological order added

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• Generalized symmetry enriched criticality in (3+1)d
• Surface topological quantum criticality: Conformal manifolds and Discrete Strong Coupling Fixed Points
• Classification and correlation signatures of chiral spin liquids on the pyrochlore lattice
• Detecting underlying symmetry-protected topological phases via strange correlators and edge engineering
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly