Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group

It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead to a better understanding of the critical physics or improve approximation schemes. However, within the framework of the non-perturbative or functional renormalization group and, in particular, of one of its most used approximation schemes, the Derivative Expansion (DE), non-trivial constraints only apply from third order (usually denoted $\mathcal{O}(\partial^4)$), at least in the usual formulation of the DE that includes correlation functions involving only the order parameter. In this work, we implement conformal constraints on a generalized DE including composite operators and show that new constraints already appear at second order of the DE (or $\mathcal{O}(\partial^2)$). We show how these constraints can be used to fix nonphysical regulator parameters.