Skyrme and Faddeev models in the low-energy limit of 4d Yang–Mills–Higgs theories

Lechtenfeld, Olaf (Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, Hannover, 30167, Germany) (Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Appelstraße 2, Hannover, 30167, Germany) ; Popov, Alexander D. (Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, Hannover, 30167, Germany)

19 June 2019

Abstract: Firstly, we consider U( Nc ) Yang–Mills gauge theory on R3,1 with Nf>Nc flavours of scalar fields in the fundamental representation of U( Nc ). The moduli space of vacua is the Grassmannian manifold Gr(Nc,Nf) . It is shown that for strong gauge coupling this 4d Yang–Mills–Higgs theory reduces to the Faddeev sigma model on R3,1 with Gr(Nc,Nf) as target. Its action contains the standard two-derivative sigma-model term as well as the four-derivative Skyrme-type term, which stabilizes solutions against scaling. Secondly, we consider a Yang–Mills–Higgs model with Nf=2Nc and a Higgs potential breaking the flavour group U(Nf)=U(2Nc) to U+(Nc)×U−(Nc) , realizing the simplest A2⊕A2 -type quiver gauge theory. The vacuum moduli space of this model is the group manifold Uh(Nc) which is the quotient of U+(Nc)×U−(Nc) by its diagonal subgroup. When the gauge coupling constant is large, this 4d Yang–Mills–Higgs model reduces to the Skyrme sigma model on R3,1 with Uh(Nc) as target. Thus, both the Skyrme and the Faddeev model arise as effective field theories in the infrared of Yang–Mills–Higgs models.


Published in: Nuclear Physics B 945 (2019) DOI: 10.1016/j.nuclphysb.2019.114675
License: CC-BY-3.0



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