The gluon condensate in an effective SU(2) Yang–Mills theory

A.N. Efremov (1)

1 CPHT - Centre de Physique Théorique [Palaiseau]

We make progress towards a derivation of a low energy effective theory for SU(2) Yang–Mills theory. This low energy action is computed to 1-loop using the renormalization group technique, taking proper care of the Slavnov–Taylor identities in the Maximal Abelian Gauge. After that, we perform the Spin-Charge decomposition in a way proposed by Faddeev and Niemi. The resulting action describes a pair of nonlinear O(3) and σ-models interacting with a scalar field. The potential of the scalar field is a Mexican hat and the location of the minima sets the energy scale of solitonic configurations of the σ-model fields whose excitations correspond to glueball states.

Mots clés: 11.10.Gh; Gluon condensate; Yang–Mills; renormalization group; effective theory; nonlinear sigma model; energy: low; gauge field theory: SU(2); sigma model: O(3); gluon: condensation; potential: scalar; Slavnov identity; effective field theory

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]

A.N. Efremov. The gluon condensate in an effective SU(2) Yang–Mills theory. International Journal of Modern Physics A, 2019, 34 (02), pp.1950018. ⟨10.1142/S0217751X19500180⟩. ⟨hal-01719626⟩