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. https://resolver.caltech.edu/CaltechAUTHORS:20160504-101448724

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Abstract

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:

URL	URL Type	Description
http://dx.doi.org/10.1007/JHEP03(2017)006	DOI	Article
http://link.springer.com/article/10.1007%2FJHEP03%282017%29006	Publisher	Article
http://arxiv.org/abs/1504.01830	arXiv	Discussion Paper

ORCID:

Author	ORCID
Kapustin, Anton	0000-0003-3903-5158
Turzillo, Alex	0000-0003-4293-4293

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

Funders:

Funding Agency	Grant Number
Simons Foundation	UNSPECIFIED
Department of Energy (DOE)	DE-SC0011632
SCOAP3	UNSPECIFIED

Subject Keywords:

Topological Field Theories; Discrete Symmetries; Topological States of Matter

Issue or Number:

DOI:

10.1007/JHEP03(2017)006

Record Number:

CaltechAUTHORS:20160504-101448724

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20160504-101448724

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

Collection:

CaltechAUTHORS

Deposited By:

Ruth Sustaita

Deposited On:

04 May 2016 20:54

Last Modified:

11 Nov 2021 00:01

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