Christian Jepsen: Noncritical and Critical O(N)r Models

mercredi 6 déc. 2023, 14:00 → 15:00 Europe/Paris

This talk will discuss the RG flows and fixed points of tensorial quantum field theories with global O(N)r symmetry, from the point of view of large N and small epsilon expansions. We will consider in turn theories with quartic and sextic interactions. For the quartic theories, we will find that the fixed points in the epsilon expansion can be matched to simple large N solutions, all dominated by vectorlike operators, whose leading Feynman diagrams are simple bubble diagrams, so that large N anomalous dimensions can be readily obtained via Hubbard-Stratonovich transforms. At general tensor rank r, the flow of vectorlike operators becomes an invariant subspace of the full RG flow and can be explicitly diagonalized, so that their fixed points can be enumerated. For the sextic theories, the large N dynamics differ qualitatively across different values of r, and we will see the appearance of a numerous and diverse set of perturbative fixed points starting at rank four.