O(N) models with boundary interactions and their long range generalizations

• Published in: The journal of high energy physics Vol. 2020; no. 8; pp. 1 - 53
• Main Authors: Giombi, Simone, Khanchandani, Himanshu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2020; Springer Nature B.V; SpringerOpen
• Subjects: Boundary Quantum Field Theory; Classical and Quantum Gravitation; Conformal Field Theory; Elementary Particles; Field theory; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativity Theory; Scalars; String Theory; Boundary Quantum Field Theory; Conformal Field Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2020)010

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.