Questions on Monopoles: t'Hooft-Polyakov & Gravity

[wasphysics]

I had a question on the t'Hooft Polyakov monopole. The issue is that since these monopoles are of finite energy shouldn't they really curve the space, so shouldn't the lagrangian (1.20) in the review paper above also have a Ricci scalar contribution and the classical field equations should be solved consistently for the g_uv, \phi and the A_\mu fields. Also what is the fate of the BPS conditions once gravity is included. Is there a reference which deals with this issue.


Also a curious nature of these solitons seems that the only way a finite energy solution could be made to exist (text between (1.30) - (1.39) ) is if the A_mu field is non-zero. This seems so D-brane like, in the sense that a d-brane exists with an open string ending on it (A_mu field). Does anyone know of references that deal with this issue.

http://arxiv.org/abs/hep-th/9603086

 

[LightHero]

The first question you asked is addressed in the paper referenced above. In particular, please see sections 3 and 4 of this reference for the consideration of gravity in the t'Hooft-Polyakov monopole. The paper also discusses the fate of the BPS conditions in the presence of gravity. With regards to your second question, it does appear that the only way to have a finite-energy solution is if the A_\mu field is non-zero. This is similar to D-branes in string theory, where the existence of a D-brane requires an open string ending on it. However, this is a rather informal observation and I am not aware of any references that address this issue explicitly.