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

This paper studies the critical behavior of the 3d classical O (N) ( N ) model with a boundary. Recently, one of us established that upon treating N N as a continuous variable, there exists a critical value N_c > 2 N c > 2 such that for 2 \leq N < N_c 2 ≤ 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 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 N c ≈ 5 . Additionally, we use semi-definite programming to place rigorous bounds on the boundary CFT data of interest to conclude that N_c > 3 N c > 3 , under a certain positivity assumption which we check in various perturbative limits.