Nonperturbative study of SU(N) Yang–Mills theory with gauge invariant condensates of mass dimension two

I study the interrelation between the dimension two gluon condensate and other phenomena occurring in SU(N) Yang–Mills theories. This condensate has turned out to be essential for a nonperturbative study of the vacuum of these theories, and it has already been studied from several points of view in the literature. This condensate gives the gluon an effective mass, offering a much needed solution to many a low-energy problem. It has turned out to be possible to study it in a renormalizable framework. I show that this framework can be extended to include background fields in the background gauge. In the seventies the vacuum of SU(2) Yang–Mills theory was found to be unstable, and a chromomagnetic field would be spontaneously generated. Such a field cannot in its turn be the end of the story either, as it not only breaks the symmetries of the theory, but also because tachyons can exist in the presence of such a field. Taking an effective gluon mass coming from the dimension two condensate into account solves this. A stable vacuum can be found, and this vacuum does not contain a chromomagnetic field any longer. In the opposite approach I find that strong chromomagnetic fields destroy the condensate. Instanton physics is also plagued by infrared problems, but this time it turns out that the condensate does not yield us a satisfactory solution. I do find that the two phenomena give separate contributions to the condensate. I also study vortices. I find strong indications that vortices have to be present in the vacuum, as they lower the vacuum energy. Finally I study the influence of temperature on the condensate. At finite temperature the electric-magnetic asymmetry also comes into the pictures. I extend the formalism to allow for this asymmetry, and I prove that this extension remains renormalizable. I compute the effective action. Minimizing it gives the temperature dependence of the condensate and its asymmetry, and the obtained results agree qualitatively with what is observed on the lattice.

Grantor dc:publisher

Ghent University. Faculty of Sciences

Year dc:date

2010

Author dc:creator

• Vercauteren, David

Contributors dc:contributor

• Verschelde, Henri

• Physics and Astronomy

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

https://biblio.ugent.be/publication/982624
https://biblio.ugent.be/publication/982624/file/4335286

OAI identifier oai:identifier

oai:archive.ugent.be:982624