Kapustin, Anton and Thorngren, Ryan (2017) Higher symmetry and gapped phases of gauge theories. In: Algebra, Geometry, and Physics in the 21st Century. Progress in Mathematics. No.324. Birkhäuser Verlag , Cham, Switzerland, pp. 177-202. ISBN 978-3-319-59938-0. https://resolver.caltech.edu/CaltechAUTHORS:20160504-081444693
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Abstract
We study topological field theory describing gapped phases of gauge theories where the gauge symmetry is partially Higgsed and partially confined. The TQFT can be formulated both in the continuum and on the lattice and generalizes Dijkgraaf–Witten theory by replacing a finite group by a finite 2-group. The basic field in this TQFT is a 2-connection on a principal 2-bundle. We classify topological actions for such theories as well as loop and surface observables. When the topological action is trivial, the TQFT is related to a Dijkgraaf–Witten theory by electric-magnetic duality, but in general it is distinct.We propose the existence of new phases of matter protected by higher symmetry.
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| Additional Information: | © 2017 Springer International Publishing AG. First Online: 29 July 2017. A.K. would like to thank Dan Freed, Sergei Gukov, Michael Hopkins, Nathan Seiberg, Yuji Tachikawa, and Constantin Teleman for discussions. R.T. would like to thank Scott Carnahan, Curt von Keyserlingk, Evan Jenkins, Alex Rasmussen, David Roberts, and Urs Schreiber for discussions. This work was supported in part by the DOE grant DE-FG02-92ER40701 and by the National Science Foundation under Grant No. PHYS-1066293 and the hospitality of the Aspen Center for Physics. | |||||||||||||||
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| Subject Keywords: | Symmetries; higher categories; topological phases of matter | |||||||||||||||
| Series Name: | Progress in Mathematics | |||||||||||||||
| Issue or Number: | 324 | |||||||||||||||
| Classification Code: | Mathematics Subject Classification (2010). 79: Mathematical Physics | |||||||||||||||
| Record Number: | CaltechAUTHORS:20160504-081444693 | |||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160504-081444693 | |||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||||||||
| ID Code: | 66633 | |||||||||||||||
| Collection: | CaltechAUTHORS | |||||||||||||||
| Deposited By: | Ruth Sustaita | |||||||||||||||
| Deposited On: | 04 May 2016 21:10 | |||||||||||||||
| Last Modified: | 03 Oct 2019 09:58 |
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