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Higher symmetry and gapped phases of gauge theories

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.

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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.

Item Type:Book Section
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URLURL TypeDescription Paper ReadCube access
Kapustin, Anton0000-0003-3903-5158
Thorngren, Ryan0000-0001-9433-3399
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.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-92ER40701
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
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66633
Deposited By: Ruth Sustaita
Deposited On:04 May 2016 21:10
Last Modified:03 Oct 2019 09:58

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