Navigating through the O(N) archipelago

Author:

Sirois Benoit12

Affiliation:

1. Institut des Hautes Études Scientifiques

2. École Normale Supérieure

Abstract

A novel method for finding allowed regions in the space of CFT-data, coined navigator method, was recently proposed in [1]. Its efficacy was demonstrated in the simplest example possible, i.e. that of the mixed-correlator study of the 3D Ising Model. In this paper, we would like to show that the navigator method may also be applied to the study of the family of dd-dimensional O(N)O(N) models. We will aim to follow these models in the (d,N)(d,N) plane. We will see that the ``sailing’’ from island to island can be understood in the context of the navigator as a parametric optimization problem, and we will exploit this fact to implement a simple and effective path-following algorithm. By sailing with the navigator through the (d,N)(d,N) plane, we will provide estimates of the scaling dimensions (\Delta_{\phi},\Delta_{s},\Delta_{t})(Δϕ,Δs,Δt) in the entire range (d,N) \in [3,4] \times [1,3](d,N)[3,4]×[1,3]. We will show that to our level of precision, we cannot see the non-unitary nature of the O(N)O(N) models due to the fractional values of dd or NN in this range. We will also study the limit N \to 1N1, and see that we cannot find any solution to the unitary mixed-correlator crossing equations below N=1N=1.

Funder

Fonds de Recherche du Québec - Nature et Technologies

Gordon and Betty Moore Foundation

Mitsubishi International Corporation

Simons Foundation

Publisher

Stichting SciPost

Subject

General Physics and Astronomy

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