# Contents

## Idea

In Yang-Mills theory and specifically in its application to QCD, the theta angle refers to the prefactor $\theta$ in the expression of the action functional of the theory in front of the piece of topological Yang-Mills theory

$\nabla \mapsto \frac{1}{g^2 }\int_X F_\nabla \wedge \star F_\nabla \;+\; i \theta \int_X F_\nabla \wedge F_\nabla$

In phenomenology the theta angle has to be very close to an integer multiple of $\pi$, see at CP problem. That it is indeed $\theta_{QCD}\simeq 0$ instead of $\theta_{QCD} \simeq \pi$ that matches experiment is argued at the end of Crewther-DiVecchia-Veneziano-Witten 79, PO discussion.
Discussion of a similar $\theta$-angle in a 3d field theory, via extended TQFT and stable homotopy theory is in
• Daniel Freed, Zohar Komargodski, Nathan Seiberg, The Sum Over Topological Sectors and $\theta$ in the 2+1-Dimensional $\mathbb{C}\mathbb{P}^1$ $\sigma$-Model (arXiv:1707.05448)