# The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap

### Submission summary

 As Contributors: Ilya Gruzberg Preprint link: scipost_202201_00004v1 Date submitted: 2022-01-10 22:55 Submitted by: Gruzberg, Ilya Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory Statistical and Soft Matter Physics Approach: Theoretical

### Abstract

This paper studies the critical behavior of the 3d classical O$(N)$ model with a boundary. Recently, one of us established that upon treating $N$ as a continuous variable, there exists a critical value $N_c > 2$ such that for $2 \leq N < N_c$ the model exhibits a new extraordinary-log boundary universality class, if the symmetry preserving interactions on the boundary are enhanced. $N_c$ is determined by a ratio of universal amplitudes in the normal universality class, where instead a symmetry breaking field is applied on the boundary. We study the normal universality class using the numerical conformal bootstrap. We find truncated solutions to the crossing equation that indicate $N_c \approx 5$. Additionally, we use semi-definite programming to place rigorous bounds on the boundary CFT data of interest to conclude that $N_c > 3$, under a certain positivity assumption which we check in various perturbative limits.

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