Comments on epsilon expansion of the O(N) model with boundary

The O$(N)$ vector model in the presence of a boundary has non-trivial fixed point $(4-\epsilon)$ dimensions and exhibits critical behaviors described by conformal field theory. spectrum operators is investigated at leading order $\epsilon$-expansion diagrammatic axiomatic approaches. In latter, we extend framework Rychkov Tan for bulk theory to case with calculate composite attention analyticity correlation functions. both approaches, obtain consistent results.