Topological field theory on a lattice, discrete theta-angles and confinement
- Creators
- Kapustin, Anton
- Thorngren, Ryan
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.
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.Attached Files
Published - ATMP-2014-0018-0005-a004.pdf
Submitted - 1308.2926v2.pdf
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Additional details
- Eprint ID
- 54329
- Resolver ID
- CaltechAUTHORS:20150203-134056790
- DE-FG02-92ER40701
- Department of Energy (DOE)
- PHY-1066293
- NSF
- Created
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2015-02-04Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field