One-loop effective action for winding configurations in SU(2)-Higgs theory

We examine the quantum correction to the static energy for Higgs winding configurations of small size. We evaluate the one-loop effective action for such configurations in Weinberg-Salam theory without U(1)-gauge fields or fermions. We use a method that, unlike derivative expansion or functional determinant methods, provides an analytic expression for the effective action in a controlled limit. For a configuration whose size, a, is much smaller than the inverse W-mass, 1/m, and the inverse Higgs mass, 1/mH , the quantum correction to the static energy of a winding configuration goes like m2a ln(1/ma)+· · ·. When mH ≫ m, the quantum correction to the static energy goes like mH 4a3 ln(1/ma) + · · ·, when a ≪ 1/m while a ∼ O(1/mH). In both scenarios, the quantum corrections to the energy are not sufficient to stabilize Higgs winding configurations. CTP#2585 Submitted to Physical Review D hep-th/9611059 Typeset in REVTEX [email protected]