Quantum Field Theory in Singular Limits

TL;DR

This paper explores the phase structure of vector O(N) symmetric quantum field theories in a singular double scaling limit, revealing a nonperturbative string theory perspective and the emergence of a dilaton as a Goldstone boson.

Contribution

It demonstrates the physical significance of the singular double scaling limit in O(N) vector theories for dimensions greater than two, linking it to nonperturbative string theory and spontaneous scale invariance breaking.

Findings

Infrared divergences compensate at each order in 1/N in the double scaling limit.

A massless O(N) singlet appears, interpreted as a dilaton from spontaneous scale invariance breaking.

The phase structure at the critical dimension involves a Goldstone boson of scale invariance.

Abstract

This is a short summary of the phase structure of vector O(N) symmetric quantum field theories in a singular limit, the double scaling limit.It is motivated by the fact that summing up dynamically triangulated random surfaces using Feynman graphs of the O(N) matrix model results in a genus expansion and it provides,in some sense, a nonperturbative treatment of string theory when the double scaling limit is enforced. The main point emphasized here is that this formal singular limit, recently discussed mainly in d=0 O(N) matrix models, has an intriguing physical meaning in d>2 O(N) vector theories. In this limit all orders in {1\over N} are of equal importance since at each order infrared divergences compensate for the decrease in powers of {1\over N}. The infrared divergences are due to the tuning of the strength of the force {g \to g_c} between the O(N) quanta so that a massless O(N) singlet appears in the spectrum. At the critical dimension an interesting phase structure is revealed, the massless excitation has the expected physical meaning: it is the Goldston boson of spontaneous breaking of scale invariance - the dilaton.