Abstract. The thermodynamics and cosmology of torus-compactified heterotic strings are studied We emphasise qualitatively new effects due to compactification New topologically stable states appear which correspond to strings winding around the non-simply-connected compact manifold Under reasonable assumptions they avoid the blowing up of the compactification scale when the universe becomes matter dominated For a higherdimensional point field theory with scale-invariant ground state this blowing up would be unavoidable
We discuss the critical bubbles of the electroweak phase transition using an effective hightemperature 3-dimensional action for the Higgs field ϕ. The separate integration of gauge and Goldstone boson degrees of freedom is conveniently described in the 't Hooft-Feynman covariant background gauge. The effective dimensionless gauge coupling g 3 (T ) 2 in the broken phase is well behaved throughout the phase transition. However, the behavior of the one-loop Z(ϕ) factors of the Higgs and gauge kinetic terms signalizes the breakdown of the derivative expansion and of the perturbative expansion for a range of small ϕ values increasing with the Higgs mass m H . Taking a functional S z [ϕ] with constant Z(ϕ) = z instead of the full non-local effective action in some neighborhood of the saddlepoint we are calculating the critical bubbles for several temperatures. The fluctuation determinant is calculated to high accuracy using a variant of the heat kernel method. It gives a strong suppression of the transition rate compared to previous estimates.
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