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

authored by

Olaf Lechtenfeld, Alexandre Popov

Abstract

Firstly, we consider U(N_c) Yang–Mills gauge theory on R^3,1 with N_f>N_c flavours of scalar fields in the fundamental representation of U(N_c). The moduli space of vacua is the Grassmannian manifold Gr(N_c,N_f). It is shown that for strong gauge coupling this 4d Yang–Mills–Higgs theory reduces to the Faddeev sigma model on R^3,1 with Gr(N_c,N_f) 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 N_f=2N_c and a Higgs potential breaking the flavour group U(N_f)=U(2N_c) to U₊(N_c)×U₋(N_c), realizing the simplest A₂⊕A₂-type quiver gauge theory. The vacuum moduli space of this model is the group manifold U_h(N_c) which is the quotient of U₊(N_c)×U₋(N_c) by its diagonal subgroup. When the gauge coupling constant is large, this 4d Yang–Mills–Higgs model reduces to the Skyrme sigma model on R^3,1 with U_h(N_c) as target. Thus, both the Skyrme and the Faddeev model arise as effective field theories in the infrared of Yang–Mills–Higgs models.

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics

Type

Artikel

Journal

Nuclear Physics B

Volume

945

ISSN

0550-3213

Publication date

08.2019

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Kern- und Hochenergiephysik

Electronic version(s)

https://doi.org/10.48550/arXiv.1808.08972 (Access: Offen)
https://doi.org/10.1016/j.nuclphysb.2019.114675 (Access: Offen)
https://doi.org/10.15488/10417 (Access: Offen)