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

by Jaychandran Padayasi, Abijith Krishnan, Max A. Metlitski, Ilya A. Gruzberg, Marco Meineri

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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Submission scipost_202201_00004v1 on 10 January 2022

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