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Generalized global symmetries

Gaiotto, Davide and Kapustin, Anton and Seiberg, Nathan and Willett, Brian (2015) Generalized global symmetries. Journal of High Energy Physics, 2015 (2). Art. No. 172. ISSN 1126-6708.

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A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries (q = 0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a sub-group). They can also have ’t Hooft anomalies, which prevent us from gauging them, but lead to ’t Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.

Item Type:Article
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URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Seiberg, Nathan0000-0003-3897-046X
Additional Information:© 2015 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: February 1, 2015. Accepted: February 1, 2015. Published: February 26, 2015. Article funded by SCOAP3. We are grateful to S. Razamat for collaboration at an early stage of the project and many important discussions. We also thank O. Aharony, N. Arkani-Hamed, J. Maldacena, G. Moore, S. Shenker, Y. Tachikawa, and E. Witten for helpful discussions. We also thank Y. Tachikawa for comments on the manuscript. The research of DG was supported by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. The work of AK was supported in part by the DOE grant DE-FG02-92ER40701 and by Simons Foundation. The work of NS was supported in part by DOE grant DE-SC0009988 and by the United States-Israel Binational Science Foundation (BSF) under grant number 2010/629. The research of BW was supported in part by DOE Grant DE-SC0009988 and the Roger Dashen Membership. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.
Funding AgencyGrant Number
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Industry CanadaUNSPECIFIED
Ontario Ministry of Economic Development and InnovationUNSPECIFIED
Department of Energy (DOE)DE-FG02-92ER40701
Simons FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0009988
Binational Science Foundation (USA-Israel)2010/629
Department of Energy (DOE)DE-SC0009988
Roger Dashen MembershipUNSPECIFIED
Subject Keywords:Global Symmetries, Wilson, ’t Hooft and Polyakov loops, Topological States of Matter, Anomalies in Field and String Theories
Issue or Number:2
Record Number:CaltechAUTHORS:20160504-105751877
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66649
Deposited By: Ruth Sustaita
Deposited On:04 May 2016 19:53
Last Modified:03 Oct 2019 09:58

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