Construction and Field Theory of Bosonic Symmetry Protected Topological states beyond Group Cohomology

TL;DR

This paper introduces a new class of bosonic symmetry protected topological states beyond traditional group cohomology, using decorated defect constructions and deriving their effective field theories.

Contribution

It develops a novel decorated defects approach to construct and analyze BSPT states beyond group cohomology classification.

Findings

Constructed BSPT states beyond group cohomology.

Derived effective field theories for these states.

Provided an intuitive physical picture of the states.

Abstract

We construct a series of bosonic symmetry protected topological (BSPT) states beyond group cohomology classification using "decorated defects" approach. This construction is based on topological defects of ordinary Landau order parameters, decorated with the bosonic short range entangled (BSRE) states in $(4k+3)d$ and $(4k+5)d$ space-time (with $k$ being nonnegative integers), which do not need any symmetry. This approach not only gives these BSPT states an intuitive physical picture, it also allows us to derive the effective field theory for all these BSPT states beyond group cohomology.