Quantum Field Theory in Singular Limits

Abstract

It has been suggested [1] to approximate geometry by dense Feynman graphs of the same topology, taking the number of vertices to infinity. The dynam ically triangulated random surfaces summed on different topologies are then viewed as the manifold for string propagation. Summing up Feynman graphs of the O(N) matrix model in d dimensions results in a genus expansion and it provides, in some sense, a nonperturbative treatment of string theory when the double scaling limit is enforced [2]. If these efforts could be extended to d > 1 dimensions, then a major progress would have been achieved in studying a long lasting problem in elementary particle theory. Namely, the relation between d dimensional quantum field theory and its possible formulation in terms of strings. The possibility of reaching a “stringy” representation of SU(N) and U(N) quantum field theory in a correlated singular limit was proposed some time ago in [3].

A Short Summary — Les Houches February 1997

This research was supported in part by a grant from the Israel Science Foundation