Conformal invariance and vector operators in the $O(N)$ model

Understand

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.