The local-potential approximation is a powerful tool to determine the RG flow in local field theories, O(N) theories being the paradigmatic example where full analytic solutions can be obtained. For fields interacting non-locally such as in tensor-invariant theories, a local potential is strictly speaking not at hand. In this talk we show under what conditions the local-potential technique is still applicable and that it can lead again to Wilson-Fisher type fixed points but also beyond.
Joseph Ben Geloun, Fabien Vignes-Tourneret