3d Large $N$ Vector Models at the Boundary

TL;DR

This paper analyzes 4d scalar fields coupled to large N boundary vector models, computing the beta function, identifying fixed points, and revealing a strong/weak duality between free and critical models, with extensions involving bulk gauge fields.

Contribution

It provides the first computation of the beta function for bulk/boundary interactions in large N vector models and uncovers a duality relating different boundary conditions.

Findings

Identifies a fixed point at infinite coupling where boundary models decouple from the bulk.

Establishes a strong/weak duality exchanging free and critical vector models.

Includes analysis of gauged models with bulk Maxwell fields and their decoupling limits.

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.