Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases
Strongly Correlated Electrons
2015-04-09 v1 High Energy Physics - Theory
Quantum Algebra
Abstract
Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify bosonic Symmetry Protected Topological Phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev's description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or less spatial dimensions are classified by twisted group cohomology, in agreement with the group cohomology proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or less are classified by ordinary group cohomology.
Keywords
Cite
@article{arxiv.1504.01830,
title = {Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases},
author = {Anton Kapustin and Alex Turzillo},
journal= {arXiv preprint arXiv:1504.01830},
year = {2015}
}