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Anyons in Geometric Models of Matter

Atiyah, Michael and Marcolli, Matilde (2017) Anyons in Geometric Models of Matter. Journal of High Energy Physics, 2017 (07). Art. No. 076. ISSN 1126-6708. https://resolver.caltech.edu/CaltechAUTHORS:20170712-085827096

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Abstract

We show that the “geometric models of matter” approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold singularities along embedded 2-dimensional surfaces. The anyon states arise through the braid representation of surface braids wrapped around the orbifold singularities, coming from multisections of the orbifold normal bundle of the embedded surface. We show that the resulting braid representations can give rise to a universal quantum computer.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/JHEP07(2017)076DOIArticle
https://link.springer.com/article/10.1007%2FJHEP07%282017%29076PublisherArticle
https://arxiv.org/abs/1611.04047arXivDiscussion Paper
Additional Information:© 2017 The Authors. 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. Received: November 22, 2016; Revised: May 28, 2017; Accepted: July 6, 2017; Published: July 14, 2017. Article funded by SCOAP3. The first author received support from the Clay Mathematical Institute, Trinity College Cambridge, and the University of Edinburgh. The second author was partially supported by NSF grants DMS-1201512 and 1707882 and PHY-1205440 and the Perimeter Institute for Theoretical Physics. The second author would also like to thank Andrew Ranicki and Ida Thompson for their generous hospitality during her visits to the first author in Edinburgh.
Funders:
Funding AgencyGrant Number
Clay Mathematical InstituteUNSPECIFIED
Trinity College CambridgeUNSPECIFIED
University of EdinburghUNSPECIFIED
NSFDMS-1201512
NSFDMS-1707882
NSFPHY-1205440
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
SCOAP3UNSPECIFIED
Subject Keywords:Anyons; Differential and Algebraic Geometry
Issue or Number:07
Record Number:CaltechAUTHORS:20170712-085827096
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170712-085827096
Official Citation:Atiyah, M. & Marcolli, M. J. High Energ. Phys. (2017) 2017: 76. https://doi.org/10.1007/JHEP07(2017)076
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78992
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Jul 2017 16:21
Last Modified:03 Oct 2019 18:14

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