Open Access
October 2014 Topological field theory on a lattice, discrete theta-angles and confinement
Anton Kapustin, Ryan Thorngren
Adv. Theor. Math. Phys. 18(5): 1233-1247 (October 2014).


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.


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Anton Kapustin. Ryan Thorngren. "Topological field theory on a lattice, discrete theta-angles and confinement." Adv. Theor. Math. Phys. 18 (5) 1233 - 1247, October 2014.


Published: October 2014
First available in Project Euclid: 25 November 2014

zbMATH: 1308.81156
MathSciNet: MR3281277

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 5 • October 2014
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