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Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases

Kapustin, Anton and Turzillo, Alex (2017) Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases. Journal of High Energy Physics, 2017 (03). Art. No. 006. ISSN 1126-6708. doi:10.1007/JHEP03(2017)006.

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Short-Range Entangled topological phases of matter are closely related to Topological Quantum Field Theory. We use this connection to classify 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 fewer spatial dimensions are classified by twisted group cohomology, in agreement with the proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or fewer are classified by ordinary group cohomology.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Turzillo, Alex0000-0003-4293-4293
Additional Information:© 2017 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: December 5, 2016; Accepted: February 14, 2017; Published: March 1, 2017. A.K. would like to thank V. Ostrik for helpful discussions. The work of A.K. was supported by the Simons Foundation. The work of A.T. was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632.
Group:Caltech Theory
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Subject Keywords:Topological Field Theories; Discrete Symmetries; Topological States of Matter
Issue or Number:03
Record Number:CaltechAUTHORS:20160504-101448724
Persistent URL:
Official Citation:Kapustin, A. & Turzillo, A. J. High Energ. Phys. (2017) 2017: 6. doi:10.1007/JHEP03(2017)006
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66642
Deposited By: Ruth Sustaita
Deposited On:04 May 2016 20:54
Last Modified:11 Nov 2021 00:01

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