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

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

Automated summary

The O(N) vector model in the presence of a boundary exhibits critical behaviors described by boundary conformal field theory in (4 - epsilon) dimensions. We investigate the spectrum of boundary operators using diagrammatic and axiomatic approaches at the leading order in the epsilon-expansion. In both approaches, consistent results are obtained, emphasizing the analyticity of correlation functions for the conformal dimensions of boundary composite operators.