nLab theta angle




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

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

(see also at S-duality for more).


In phenomenology the theta angle has to be very close to an integer multiple of π\pi, see at CP problem. That it is indeed θ QCD0\theta_{QCD}\sim 0 instead of θ QCDπ\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)

L D4 WZC 1FF. \mathbf{L}_{D4}^{WZ} \;\propto\; C_1 \wedge \langle F \wedge F\rangle \,.



Discussion of a similar θ\theta-angle in a 3d field theory, via extended TQFT and stable homotopy theory is in

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 θ\theta-angle as the graviphoton RR-field-potential C 1C_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 June 1, 2020 at 18:17:57. See the history of this page for a list of all contributions to it.