Exotic invertible phases with highergroup symmetries
Abstract
We investigate a family of invertible phases of matter with higherdimensional exotic excitations in even spacetime dimensions, which includes and generalizes the Kitaev's chain in 1+1d. The excitation has \mathbb{Z}_2&Z;2 higherform symmetry that mixes with the spacetime Lorentz symmetry to form a higher group spacetime symmetry. We focus on the invertible exotic loop topological phase in 3+1d. This invertible phase is protected by the \mathbb{Z}_2&Z;2 oneform symmetry and the timereversal symmetry, and has surface thermal Hall conductance not realized in conventional timereversal symmetric ordinary bosonic systems without local fermion particles and the exotic loops. We describe a UV realization of the invertible exotic loop topological order using the SO(3)_SO(3)− gauge theory with unit discrete theta parameter, which enjoys the same spacetime twogroup symmetry. We discuss several applications including the analogue of ``fermionization'' for ordinary bosonic theories with \mathbb{Z}_2&Z;2 nonanomalous internal higherform symmetry and timereversal symmetry.
 Publication:

SciPost Physics
 Pub Date:
 February 2022
 DOI:
 10.21468/SciPostPhys.12.2.052
 arXiv:
 arXiv:2105.09454
 Bibcode:
 2022ScPP...12...52H
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 62 pages, 4 figures, 3 tables