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 1N→1,
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
Subject
General Physics and Astronomy
Cited by
3 articles.
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