Resummation and renormalons in a general Quantum Field Theory.

We generalize the concept of Borel resummability and renormalons to a quantum field theory with an arbitrary number of fields and couplings, starting from the known notion based on the running coupling constant in the one-field model. An approach to identify the renormalons is provided by exploiting an analytic solution of the generic one-loop renormalization group equations in multi-field theories. Methods to evaluate the regions in coupling space where the theory is resummable are described. The generalization is then illustrated in a toy model with two coupled scalar fields, representing the simplest extension of the one-field analysis presented in the seminal works of the subject. Furthermore, possible links to realistic models are briefly discussed.