Euclidean solutions of Yang–Mills theory coupled to a massive dilaton

George Lavrelashvili,Yves Brihaye

doi:10.1016/j.physletb.2007.09.051

Abstract

The Euclidean version of the Yang–Mills theory coupled to a massive dilaton is investigated. Our analytical and numerical results implies the existence of an infinite number of branches of globally regular, spherically symmetric, dyonic type solutions. The solutions exist for m⩾0, where m denotes the mass of the dilaton field, and the different branches are labeled by the number of nodes of the gauge field function W. They have a finite action and provide new saddle points, relevant in the Euclidean path integral.

Highlights

Motivated mainly by the Bartnik-McKinnon discovery [1] of globally regular, static, spherically symmetric solutions of the Einstein-Yang-Mills (EYM) equations and similar results obtained in the EYM and YM theory coupled to a dilaton field [2, 3, 4, 5, 6, 7] the Euclidean version of the EYM and YM theory coupled to a dilaton were investigated recently [8], [9]
Since close to the minimum potential can be well approximated by the dilaton mass term it is of certain interest to investigate Euclidean solutions in the YM theory coupled to a massive dilaton, which is exactly the aim of present Letter
In the present study we investigated O(3)−symmetric solutions of four dimensional Euclidean YMD theory and found branches of dyonic type solutions for any values of dilaton mass m

Summary

INTRODUCTION

Motivated mainly by the Bartnik-McKinnon discovery [1] of globally regular, static, spherically symmetric solutions of the Einstein-Yang-Mills (EYM) equations and similar results obtained in the EYM and YM theory coupled to a dilaton field [2, 3, 4, 5, 6, 7] the Euclidean version of the EYM and YM theory coupled to a dilaton were investigated recently [8], [9]. While in the four dimensional space-time with Lorentzian signature electric part of non-abelian SU(2) gauge field should necessarily vanish for asymptotically flat solutions [10, 11] situation is changed in Euclidean sector: electric field here plays role similar to the Higgs field of the Lorentzian sector [12] and there are nontrivial dyonic type solutions [8], [9]. Dilaton field in these investigations was considered to be massless.

THE MODEL

The Ansatz and equations

Asymptotic behaviour

SPECIAL SOLUTIONS

NUMERICAL RESULTS

Zero-node solutions

Solutions with the nodes

CONCLUDING REMARKS