TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.3.090
TI  - A plane defect in the 3d O(N) model
PY  - 2023/09/12
UR  - https://scipost.org/SciPostPhys.15.3.090
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 3
SP  - 090
A1  - Krishnan, Abijith
AU  - Metlitski, Max A.
AB  - It was recently found that the classical 3d O$(N)$ model in the semi-infinite geometry can exhibit an "extraordinary-log" boundary universality class, where the spin-spin correlation function on the boundary falls off as $\langle \vec{S}(x) \cdot \vec{S}(0)\rangle \sim \frac{1}{(\log x)^q}$. This universality class exists for a range $2 ≤ N < N_c$ {and Monte-Carlo simulations and conformal bootstrap} indicate $N_c > 3$. In this work, we extend this {result} to the 3d O$(N)$ model in an infinite geometry with a plane defect. We use renormalization group (RG) to show that in this case the extraordinary-log universality class is present for any finite $N ≥ 2$. We additionally show, {in agreement with our RG analysis}, that the line of defect fixed points which is present at $N = ∞$ is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by $1/N$ corrections. We study the "central charge" $a$ for the $O(N)$ model in the boundary and interface geometries and provide a non-trivial detailed check of an $a$-theorem by Jensen and O'Bannon. Finally, we revisit the problem of the O$(N)$ model in the semi-infinite geometry. We find evidence that at $N = N_c$ the extraordinary and special fixed points annihilate and only the ordinary fixed point is left for $N > N_c$.
ER  -

@Article{10.21468/SciPostPhys.15.3.090,
	title={{A plane defect in the 3d O(N) model}},
	author={Abijith Krishnan and Max A. Metlitski},
	journal={SciPost Phys.},
	volume={15},
	pages={090},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.3.090},
	url={https://scipost.org/10.21468/SciPostPhys.15.3.090},
}