Topological field theory on a lattice, discrete theta-angles and confinement. (English) Zbl 1308.81156

Kapustin, Anton; Thorngren, Ryan

Adv. Theor. Math. Phys. 18, No. 5, 1233-1247 (2014).

Summary: 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.

MSC:

81T45	Topological field theories in quantum mechanics
81T25	Quantum field theory on lattices
81T13	Yang-Mills and other gauge theories in quantum field theory