$O(N)$ Models with Boundary Interactions and their Long Range Generalizations

Understand

We study the critical properties of scalar field theories in $d+1$ dimensions with $O(N)$ invariant interactions localized on a $d$-dimensional boundary.

• By a combination of large $N$ and epsilon expansions, we provide evidence for the existence of non-trivial $O(N)$ BCFTs in $1<d<4$.
• Due to having free fields in the bulk, these models possess bulk higher-spin currents which are conserved up to terms localized on the boundary.
• We suggest that this should lead to a set of protected spinning operators on the boundary, and give evidence that their anomalous dimensions vanish.