Contents

# 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

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

## Phenomenology

In phenomenology the theta angle has to be very close to an integer multiple of $\pi$, see at CP problem. That it is indeed $\theta_{QCD}\sim 0$ instead of $\theta_{QCD} \sim \pi$ that matches experiment is argued at the end of Crewther-DiVecchia-Veneziano-Witten 79, PO discussion.

## In string theory and AdS/QCD

Within string theory, with Yang-Mills theory realized on intersecting D-brane models, as on D4-branes for holographic QCD, the theta angle corresponds to the graviphoton RR-field 1-form potential in the higher WZW term of the D4-brane, which is (CGNSW 96 (7.4) APPS97b (51), CAIB 99, 6.1)

$\mathbf{L}_{D4}^{WZ} \;\propto\; C_1 \wedge \langle F \wedge F\rangle \,.$

## References

### General

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)

In relation to confinement:

• Massimo D’Elia, Francesco Negro, Theta dependence of the deconfinement temperature in Yang-Mills theories, Phys. Rev. Lett. 109, 2012 (arXiv:1205.0538)

### In string theory

The $\theta$-angle as the graviphoton RR-field-potential $C_1$ in the higher WZW term of the D4-brane:

For more see at Green-Schwarz sigma model – References – For D-branes.

Discussion explicitly in view of the Witten-Sakai-Sugimoto model for QCD on D4-branes:

• Si-wen Li, around (3.1) of The theta-dependent Yang-Mills theory at finite temperature in a holographic description (arXiv:1907.10277)

Last revised on July 26, 2019 at 05:27:12. See the history of this page for a list of all contributions to it.