The sine-Gordon model and the small. kappa. sup + region of light- cone perturbation theory

Abstract

The non-perturbative ultraviolet divergence of the sine-Gordon model is used to study the k{sup +} = 0 region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the non- perturbative {beta}{sup 2} = 8{pi} critical point by a light-cone version of Coleman's variational method. Vacuum bubbles, which are k{sup +} = 0 diagram in light-cone field theory and are individually finite and non-vanishing for all {beta}, conspire to generate ultraviolet divergences of the light-cone energy density. The k{sup +} = 0 region of momentum also contributed to connected Green's functions: the connected two point function will not diverge, as it should, at the critical point unless diagrams which contribute only at k {sup +} = 0 are properly included. This analysis shows in a simple way how the k {sup +} = 0 region cannot be ignored even for connected diagrams. This phenomenon is expected to occur in higher dimensional gauge theories starting at two loop order in light-cone perturbation theory.