Navigating through the O(N) archipelago
Benoit Sirois
SciPost Phys. 13, 081 (2022) · published 4 October 2022
- doi: 10.21468/SciPostPhys.13.4.081
- Submissions/Reports
Abstract
A novel method for finding allowed regions in the space of CFT-data, coined navigator method, was recently proposed in arXiv:2104.09518. 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 $d$-dimensional $O(N)$ models. We will aim to follow these models in the $(d,N)$ 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 $(d,N)$ plane, we will provide estimates of the scaling dimensions $(\Delta_{\phi},\Delta_{s},\Delta_{t})$ in the entire range $(d,N) \in [3,4] \times [1,3]$. We will show that to our level of precision, we cannot see the non-unitary nature of the $O(N)$ models due to the fractional values of $d$ or $N$ in this range. We will also study the limit $N \xrightarrow[]{} 1$, and see that we cannot find any solution to the unitary mixed-correlator crossing equations below $N=1$.
Cited by 3
Author / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 Benoit Sirois
- Fonds de Recherche du Québec - Nature et Technologies (through Organization: Fonds de Recherche du Québec – Nature et technologies [FRQNT])
- Gordon and Betty Moore Foundation
- Mitsubishi International Corporation (through Organization: 三菱重工業株式会社 / Mitsubishi Heavy Industries (Japan) [MHI])
- Simons Foundation