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

Author(s): Giombi, Simone; Khanchandani, Himanshu

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Abstract: 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.
Publication Date: 4-Aug-2020
Electronic Publication Date: 4-Aug-2020
Citation: Giombi, Simone, Khanchandani, Himanshu. (2020). O(N) models with boundary interactions and their long range generalizations. Journal of High Energy Physics, 2020 (8), 10.1007/jhep08(2020)010
DOI: doi:10.1007/jhep08(2020)010
EISSN: 1029-8479
Keywords: Boundary Quantum Field Theory, Conformal Field Theory
Language: en
Type of Material: Journal Article
Journal/Proceeding Title: Journal of High Energy Physics
Version: Final published version. This is an open access article.

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