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Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology

Kapustin, Anton (2014) Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20160504-095515747

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Abstract

We propose that Symmetry Protected Topological Phases with a finite symmetry group G are classified by cobordism groups of the classifying space of G. This provides an explanation for the recent discovery of bosonic SPT phases which do not fit into the group cohomology classification. We discuss the connection of the cobordism classification of SPT phases to gauge and gravitational anomalies in various dimensions.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1403.1467arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Additional Information:(Submitted on 6 Mar 2014 (v1), last revised 14 Apr 2014 (this version, v3)). April 16, 2014. I am would like to thank Ryan Thorngren for a collaboration on a related project, Dan Freed for drawing my attention to cobordism groups, and John Morgan and Michael Hopkins for advice. I am especially grateful to Alexei Kitaev for pointing out a number of erroneous statements in the first version of the manuscript. This work was supported in part by the DOE grant DE-FG02-92ER40701.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-92ER40701
Record Number:CaltechAUTHORS:20160504-095515747
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160504-095515747
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66638
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:04 May 2016 21:00
Last Modified:27 Oct 2017 18:14

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