The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
This paper studies the critical behavior of the 3d classical \(\mathrm{O}(N)\) 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 extraordi...
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| creator | Padayasi, Jaychandran Krishnan, Abijith Metlitski, Max A Gruzberg, Ilya A Meineri, Marco |
| description | This paper studies the critical behavior of the 3d classical \(\mathrm{O}(N)\) 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. |
| doi_str_mv | 10.48550/arxiv.2111.03071 |
| format | Article |
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| title | The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap |
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