INSTANTONS FOR VACUUM DECAY AT FINITE-TEMPERATURE IN THE THIN WALL LIMIT

In N + 1 dimensions, false vacuum decay at zero temperature is dominat ed by the O(N + 1)-symmetric instanton, a sphere of radius Ro, whereas at temperatures T much greater than R0(-1), the decay is dominated by a ''cylindrical'' (static) O(N)-symmetric instanton. We study the tra nsition between these two regimes in the thin wall approximation. Taki ng an O(N)-symmetric ansatz for the instantons, we show that for N = 2 and N = 3 new periodic solutions exist in a finite temperature range in the neighborhood of T approximately R0(-1). However, these solution s have a higher action than the spherical or the cylindrical one. This suggests that there is a sudden change (a first order transition) in the derivative of the nucleation rate at a certain temperature T., whe n the static instanton starts dominating. For N = 1, on the other hand , the new solutions are dominant and they smoothly interpolate between the zero temperature instanton and the high temperature one, so the t ransition is of second order. The determinantal prefactors correspondi ng to the ''cylindrical'' instantons are discussed, and it is pointed out that the entropic contributions from massless excitations correspo nding to deformations of the domain wall give rise to an exponential e nhancement of the nucleation rate for T much-greater-than R0(-1).