The sine-Gordon model and the small k^+ region of light-cone perturbation theory

Abstract

The non-perturbative ultraviolet divergence of the sine-Gordon model is used to study the $k^{+}=0$ region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the non-perturbative ${\beta }^2=8\pi$ critical point by a light-cone version of Coleman's variational method. Vacuum bubbles, which are $k^{+}=0$ diagrams 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 $k^{+}=0$ region of momentum also contributes 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 $k^{+}=0$ are properly included. This analysis shows in a simple way how the $k^{+}=0$ 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.

8 pages, UFIFT-HEP-92-17

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