## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 18, Number 5 (2014), 1233-1247.

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

Anton Kapustin and Ryan Thorngren

#### 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.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 18, Number 5 (2014), 1233-1247.

**Dates**

First available in Project Euclid: 25 November 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1416929532

**Mathematical Reviews number (MathSciNet)**

MR3281277

**Zentralblatt MATH identifier**

1308.81156

#### Citation

Kapustin, Anton; Thorngren, Ryan. Topological field theory on a lattice, discrete theta-angles and confinement. Adv. Theor. Math. Phys. 18 (2014), no. 5, 1233--1247. https://projecteuclid.org/euclid.atmp/1416929532