## 3d large $N$ vector models at the boundary

Lorenzo Di Pietro, Edoardo Lauria, Pierluigi Niro

SciPost Phys. 11, 050 (2021) · published 8 September 2021

- doi: 10.21468/SciPostPhys.11.3.050
- Submissions/Reports

### Abstract

We consider a 4d scalar field coupled to large $N$ free or critical $O(N)$ vector models, either bosonic or fermionic, on a 3d boundary. We compute the $\beta$ function of the classically marginal bulk/boundary interaction at the first non-trivial order in the large $N$ expansion and exactly in the coupling. Starting with the free (critical) vector model at weak coupling, we find a fixed point at infinite coupling in which the boundary theory is the critical (free) vector model and the bulk decouples. We show that a strong/weak duality relates one description of the renormalization group flow to another one in which the free and the critical vector models are exchanged. We then consider the theory with an additional Maxwell field in the bulk, which also gives decoupling limits with gauged vector models on the boundary.

### Cited by 9

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Lorenzo Di Pietro, -
^{3}Edoardo Lauria, -
^{4}^{5}Pierluigi Niro

^{1}Università degli Studi di Trieste / University of Trieste [UNITS]^{2}INFN Sezione di Trieste / INFN Trieste^{3}Centre de Physique Théorique / Center of Theoretical Physics [CPHT]^{4}Université Libre de Bruxelles [ULB]^{5}International Solvay Institutes

- Fonds De La Recherche Scientifique - FNRS (FNRS) (through Organization: Fonds National de la Recherche Scientifique [FNRS])
- Instituto Nazionale di Fisica Nucleare (INFN) (through Organization: Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN])
- Simons Foundation