Alien calculus and a Schwinger--Dyson equation: two-point function with a nonperturbative mass scale

Understand

Starting from the Schwinger--Dyson equation and the renormalization group equation for the massless Wess--Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points.

• The sum of these dominant contributions has an analytic expression.
• When applied to the two-point function, this analysis gives a tame evolution in the deep euclidean domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive \(\beta\)-function.
• On the other side, we have a singularity of the propagator for time like momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory.