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

Abstract

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 L.D. Faddeev and A.J. Niemi. The resulting action describes a pair of non-linear O(3) nonlinear sigma 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 sigma model fields whose excitations correspond to glueball states.

References in corpus (11)

• Knots and Particles
• Partially Dual variables in SU(2) Yang-Mills Theory
• On the Significance of the Quantity "A Squared"
• Vacuum condensate of mass dimension 2 as the origin of mass gap and quark confinement
• Knots in the Skyrme-Faddeev model
• Spin-Charge Separation, Conformal Covariance and the SU(2) Yang-Mills Theory
• Wilsonian effective action for SU(2) Yang-Mills theory with Cho-Faddeev-Niemi-Shabanov decomposition
• Fixed Points of Nonlinear Sigma Models in d>2
• Renormalization of SU(2) Yang-Mills theory with Flow Equations
• All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory
• Composite operator and condensate in the $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group