Real-time correlation functions in the $$O(N)$$ O ( N ) model from the functional renormalization group

In the framework of the functional renormalization group we present a simple truncation scheme for the computation of real-time mesonic n -point functions, consistent with the derivative expansion of the effective action. Via analytic continuation on the level of the flow equations we perform calculations of mesonic spectral functions in the scalar $$O(N)$$ model, which we use as an exploratory example. By investigating the renormalization-scale dependence of the 2-point functions we shed light on the nature of the sigma meson, whose spectral properties are predominantly of dynamical origin.