Conformal invariance and vector operators in the $O(N)$ model
| Autor: | Nicolás Wschebor, Gonzalo De Polsi, Matthieu Tissier |
|---|---|
| Přispěvatelé: | Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
invariance: conformal operator: vector Vector operator FOS: Physical sciences expansion: derivative Scaling dimension 01 natural sciences 010305 fluids & plasmas Conformal symmetry 0103 physical sciences Ising model correlation function renormalization group: nonperturbative 010306 general physics Scaling Mathematical Physics Condensed Matter - Statistical Mechanics Mathematical physics Mathematics scaling: dimension Statistical Mechanics (cond-mat.stat-mech) [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] Statistical and Nonlinear Physics Invariant (physics) Scale invariance O(N) 16. Peace & justice [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] symmetry: internal High Energy Physics - Theory (hep-th) Homogeneous space perturbation: vector |
| Zdroj: | J.Statist.Phys. J.Statist.Phys., 2019, 177, pp.1089. ⟨10.1007/s10955-019-02411-3⟩ |
| DOI: | 10.1007/s10955-019-02411-3⟩ |
| Popis: | It is widely expected that, for a large class of models, scale invariance implies conformal invariance. A sufficient condition for this to happen is that there exists no integrated vector operator, invariant under all internal symmetries of the model, with scaling dimension $-1$. In this article, we compute the scaling dimensions of vector operators with lowest dimensions in the $O(N)$ model. We use three different approximation schemes: $\epsilon$ expansion, large $N$ limit and third order of the Derivative Expansion of Non-Perturbative Renormalization Group equations. We find that the scaling dimensions of all considered integrated vector operators are always much larger than $-1$. This strongly supports the existence of conformal invariance in this model. For the Ising model, an argument based on correlation functions inequalities was derived, which yields a lower bound for the scaling dimension of the vector perturbations. We generalize this proof to the case of the $O(N)$ model with $N\in \left\lbrace 2,3,4 \right\rbrace$. Comment: 43 pages, 7 figures. This version includes some of the material previously included in arXiv:1804.08374 |
| Databáze: | OpenAIRE |
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