Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2012-01-25
Physics
High Energy Physics
High Energy Physics - Theory
23 pages, introduction and conclusion are expanded; some references are added. This is the version accepted by J. Phys. A
Scientific paper
We study the stability of a non-Abelian chromomagnetic vacuum in Yang-Mills theory in Euclidean Einstein universe $S^1\times S^3$. We assume that the gauge group is a simple compact group $G$ containing the group SU(2) as a subgroup and consider static covariantly constant gauge fields on $S^3$ taking values in the adjoint representation of the group $G$ and forming a representation of the group SU(2)$. We compute the heat kernel for the Laplacian acting on fields on $S^3$ in an arbitrary representation of SU(2) and use this result to compute the heat kernels for the gluon and the ghost operators and the one-loop effective action. We show that the only configuration of the covariantly constant Yang-Mills background that is stable is the one that contains only spinor (fundamental) representations of the group SU(2); all other configurations contain negative modes and are unstable. For the stable configuration we compute the asymptotics of the effective action, the energy density, the entropy and the heat capacity in the limits of low/high temperature and small/large volume and show that the energy density has a non-trivial minimum at a finite value of the radius of the sphere $S^3$.
Avramidi Ivan G.
Collopy Samuel
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