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Topological field theory on a lattice, discrete theta-angles and confinement

Kapustin, Anton and Thorngren, Ryan (2014) Topological field theory on a lattice, discrete theta-angles and confinement. Advances in Theoretical and Mathematical Physics, 18 (5). pp. 1233-1247. ISSN 1095-0761. https://resolver.caltech.edu/CaltechAUTHORS:20150203-134056790

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Abstract

We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group (the magnetic gauge group). We show that possible theta-angles in such a theory are quantized and labeled by quadratic functions on the magnetic gauge group. When the theta-angles vanish, the theory is dual to an ordinary topological gauge theory, but in general it is not isomorphic to it. We also explain how to couple a lattice Yang-Mills theory to a TQFT of this kind so that the ’t Hooft flux is well-defined, and quantized values of the theta-angles are allowed. The quantized theta-angles include the discrete theta-angles recently identified by Aharony, Seiberg and Tachikawa.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.4310/ATMP.2014.v18.n5.a4DOIArticle
http://www.intlpress.com/site/pub/pages/journals/items/atmp/content/vols/0018/0005/a004/PublisherArticle
http://arxiv.org/abs/1308.2926arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Thorngren, Ryan0000-0001-9433-3399
Additional Information:© 2014 International Press of Boston, Inc. A.K. would like to thank Dan Freed, Sergei Gukov, Michael Hopkins, Nathan Seiberg, Yuji Tachikawa, and Constantin Teleman for discussions. R.T. would also like to thank Scott Carnahan, 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.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-92ER40701
NSFPHY-1066293
Issue or Number:5
Record Number:CaltechAUTHORS:20150203-134056790
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150203-134056790
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54329
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:04 Feb 2015 21:45
Last Modified:03 Oct 2019 07:56

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