Conformal Invariance of the large-$N$ limit of the $O(N)$ universality class

Santiago Cabrera; Gonzalo De Polsi; Adam Rançon; Nicolás Wschebor

doi:10.1103/yznz-gcqs

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arXiv · 2604.24675

Conformal Invariance of the large-$N$ limit of the $O(N)$ universality class

Santiago Cabrera·Gonzalo De Polsi·Adam Rançon·Nicolás Wschebor

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Abstract

Conformal symmetry is expected to be realized in many equilibrium statistical mechanical systems at criticality. Although this is certainly true in two-dimensional systems, the three-dimensional case is subtler, and only a few proofs exist, only so in very specific cases. In this work, we give two proofs for the large $N$ limit of the $O(N)$ universality class within the non-perturbative renormalization group framework: one functional, and one vertex-by-vertex in Fourier space. While doing so, we unveil how the theory is structured in order for conformal symmetry to be realized. As a consequence, we shed light on what to expect, on rather general grounds, for a theory to be conformally invariant.

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Santiago Cabrera, Gonzalo De Polsi, Adam Rançon, Nicolás Wschebor. 2026-04-27. Conformal Invariance of the large-$N$ limit of the $O(N)$ universality class. https://doi.org/10.1103/yznz-gcqs

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