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

Tatsuma Nishioka; Yoshitaka Okuyama; Soichiro Shimamori

doi:10.1007/jhep03(2023)051

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arXiv · 2212.04078

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

Tatsuma Nishioka·Yoshitaka Okuyama·Soichiro Shimamori

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Abstract

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.

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Tatsuma Nishioka, Yoshitaka Okuyama, Soichiro Shimamori. 2022-12-08. Comments on epsilon expansion of the O$(N)$ model with boundary. https://doi.org/10.1007/jhep03(2023)051

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