Two dimensional renormalization group flows in next to leading order

Zamolodchikov’s famous analysis of the RG trajectory connecting successive minimal CFT models Mp and Mp−1 for p ≫ 1, is improved by including second order in coupling constant corrections. This allows to compute IR quantities with next to leading order accuracy of the 1/p expansion. We compute in particular, the beta function and the anomalous dimensions for certain classes of fields. As a result we are able to identify with a greater accuracy the IR limit of these fields with certain linear combination of the IR theory Mp−1. We discuss the relation of these results with Gaiotto’s recent RG domain wall proposal.