Generalized global symmetries

Abstract

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.

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© 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.

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