Long-Range Vector Models at Large N

TL;DR

This paper computes conformal field theory data for the long-range $O(N)$ vector model at large N, providing evidence for conformal symmetry, the crossover behavior, and a proposed IR duality between long-range and short-range models.

Contribution

It extends the analysis of the long-range $O(N)$ model to next-to-leading order in 1/N, and generalizes the IR duality to the $N>1$ case, supporting its non-perturbative validity.

Findings

Evidence for conformal symmetry at the long-range fixed point

Continuity of CFT data at the crossover point $s_*$

Support for the IR duality between long-range and deformed short-range models

Abstract

We calculate various CFT data for the $O(N)$ vector model with the long-range interaction, working at the next-to-leading order in the $1/N$ expansion. Our results provide additional evidence for the existence of conformal symmetry at the long-range fixed point, as well as the continuity of the CFT data at the long-range to short-range crossover point $s_\star$ of the exponent parameter $s$. We also develop the $N>1$ generalization of the recently proposed IR duality between the long-range and the deformed short-range models, providing further evidence for its non-perturbative validity in the entire region $d/2<s<s_\star$.