Numerical evidence for the existence of a novel magnetic condensation in Yang-Mills theory

Abstract

We present a first numerical evidence for the existence of a novel magnetic condensate proposed recently by one of the authors in SU(2) Yang-Mills theory. In our framework, the spontaneously generated color magnetic field identified with the Savvidy vacuum has the microscopic origin and is a consequence of the intrinsic dynamics of the Yang-Mills theory. It strongly suggests the Nielsen--Olesen instability of the Savvidy vacuum disappears and the stability is restored without the need of the Copenhagen vacuum. The implications to the Faddeev-Skyrme model are also discussed. These results are obtained through the first implementation of the Cho--Faddeev--Niemi decomposition of the Yang-Mills field on a lattice.

2+36 pages, 13 figures; no change of conclusion, Introduction and Sec. 3.1.2 are improved, Sec. 4.8 is added, Discussion is supplemented by remarks on the gauge invariance, Appendix A.2 is added, A.1 and A.3 are simplified, references [3][4][12][33][51][52] are added, typos are corrected; numerous minor changes of presentations