O(N) Vector Models in the Limit $g\to g_c$ and Finite Temperature

Abstract

In the limit where $N\to \infty$ and the coupling constant $g\to g_c$ in a correlated manner, O(N) symmetric vector models represent filamentary surfaces. The purpose of these studies is to gain intuition for the long lasting search for a possible description of quantum field theory in terms of extended objects. It is shown here that a certain limiting procedure has to be followed in order to avoid several difficulties in establishing the theory at a critical negative coupling constant. It is also argued that at finite temperature a certain metastable-false vacuum disappears as the temperature is increased.

(Summary of a talk at Banff Workshope) (5 pages)