O(N) models with boundary interactions and their long range generalizations
Simone Giombi, Himanshu Khanchandani
Abstract
A bstract 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. We also discuss the closely related long-range O( N ) models in d dimensions, and in particular study a weakly coupled description of the d = 1 long range O( N ) model near the upper critical value of the long range parameter, which is given in terms of a non-local non-linear sigma model. By combining the known perturbative descriptions, we provide some estimates of critical exponents in d = 1.