On the Double Scaling Limit of O(N) Vector Models in d=2

TL;DR

This paper investigates the double scaling limit of O(N) vector models in two dimensions, revealing that the absence of massless bound states imposes significant constraints on the behavior of these models in the limit.

Contribution

It provides a detailed analysis of the double scaling limit in O(N) vector models in two dimensions, highlighting the impact of the absence of massless bound states.

Findings

Absence of physical massless bound states in d=2 constrains the double scaling limit.

Explicit calculations of filamentary surface expansions in d≥2.

Constraints on the large N limit due to mass gap considerations.

Abstract

Recent interest in large N matrix models in the double scaling limit raised new interest also in O(N) vector models. The limit $N \rightarrow \infty$, correlated with the limit $g \rightarrow g_c$, results in an expansion in terms of filamentary surfaces and explicit calculations can be carried out also in dimensions $d\geq 2$. It is shown here that the absence of physical massless bound states in two dimensions sets strong constraints on this limit.