BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Space-dependent RG, anomalous dimensions in a hierarchical model for 3d CFT and connections to the AdS/CFT correspondence Abdesselam, Abdelmalek


(Joint work with Ajay Chandra and Gianluca Guadagni)

An outstanding problem in the area of rigorous renormalization group theory is to develop a Wilsonian formalism which can handle space-dependent couplings in the Euclidean setting. I will present such a method in the simpler hierarchical model case and explain how this allowed us to prove a 46 years old prediction by Wilson regarding the anomalous scaling of the square/energy field in a hierarchical ferromagnet.

The model we studied is a hierarchical version of a 3d ferromagnet with long-range interactions in a range of parameters which puts it slightly below the upper critical dimension. We constructed the scaling limit for the joint law of the elementary/spin field together with the square/energy field as well as all mixed correlation functions. The Euclidean version of this scaling limit is conjectured to be a conformal field theory in three dimensions according to recent work by physicists in the conformal bootstrap program. There is a natural analogue of conformal invariance in the hierarchical model which thus provides an ideal testing ground for renormalization group-based attempts at rigorously proving conformal invariance. The idea is to feed the space-dependent renormalization group space-dependent ultraviolet cutoffs. I will also mention emerging connections to the AdS/CFT correspondence.

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