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A plane defect in the 3d O(N) model
by Abijith Krishnan, Maxim A. Metlitski
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Submission summary
| Authors (as registered SciPost users): | Abijith Krishnan |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202304_00015v1 (pdf) |
| Date submitted: | 2023-04-14 18:35 |
| Submitted by: | Krishnan, Abijith |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
{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 $2 \leq N < N_c$ {and Monte-Carlo simulations and conformal bootstrap} indicate $N_c > 3$. In this work, we extend this %analysis {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 $N \ge 2$. We additionally show, {in agreement with our RG analysis}, that the line of defect fixed points which is present at $N = \infty$ is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by $1/N$ corrections. %in agreement with our RG analysis. {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 $N > N_c$.
Current status:
Reports on this Submission
Anonymous Report 2 on 2023-6-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202304_00015v1, delivered 2023-06-08, doi: 10.21468/SciPost.Report.7325
Strengths
- Extremely interesting topic. The paper focuses on the phase diagram of defect CFTs in the O(N) model, and in particular, on an unusual universality class that exhibits logarithmic behavior in the spin two-point function.
- Detailed RG and perturbative calculations that clarify the picture, and serve as check for several of the claims made in the paper.
- Nice pictures and plots.
Weaknesses
None
Report
This paper studies the ''extraordinary log'' universality class for defects in the O(N) model. This class is characterized by a spin two-point function that falls off logarithmically, as opposed to the more standard power-law behavior. This extremely interesting universality class had been studied for BCFT in the O(N) model, and the analysis is now extended to the case of an interface. The main result of the paper is that log universality class is expected for any N>=2, while for BCFT it was constrained to a range.
The paper contains careful perturbative calculations with a lot of details. In addition to studying the phase diagram, the authors also check the consistency of their results with the defect version of the a-theorem. As far as I can tell, everything looks solid.
This is an excellent paper, full of interesting results. I strongly recommend it for publication
Requested changes
No changes from my part
Anonymous Report 1 on 2023-5-12 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202304_00015v1, delivered 2023-05-12, doi: 10.21468/SciPost.Report.7184
Strengths
1 - The paper extends a recent important result on the boundary criticality of the O(N) model to the case of a critical interface. The result is qualitatively different from the boundary case, providing evidence for the existence of an extraordinary-log class for all N>=2, which is remarkable.
2 - It also includes relevant results on how the possible interface RG flows are consistent with monotonicity theorem, as well as providing strong evidence for the form of the phase diagram in the boundary case, suggested in previous work.
3 - A very well-written introduction gives a good summary of all the different results and provides a coherent picture of the full paper.
Weaknesses
1 - Each section feels a bit too independent of the others, since they cover somewhat different aspects. This is mitigated by the excellent introduction.
Report
The paper presents new and interesting results on both conformal boundaries and conformal interfaces of the critical 3d O(N) model. It gives evidence for the existence of an extraordinary-log interface universality class for all N>=2, in opposition to the boundary case where this only happens in a window 2<=N<N_c .
The manuscript complements this result with an in-depth analysis of interface RG flows using monotonicity theorems, as well as computing a key quantity (at large N) in the boundary case, which gives evidence for the detailed form of the phase diagram in the 2<=N<N_c range.
The paper is overall of excellent quality and I recommend it for Publication.
I do have some questions and suggestions that might help further clarify certain points, but my recommendation for publication is not contingent on the authors addressing them.
Requested changes
1 - In page 4 below eq 1.3, it is said that "believed that the scaling dimension ∆ϵ < 2 for all finite N ≥ 1". It might be worth pointing out the existence of rigorous bootstrap bounds which show this for many values of N, including moderately large N.
2 - In page 16 it is said that "the
interface ordinary fixed point is equivalent to two decoupled boundary ordinary fixed points for each
side of the interface". Reminding the reader of eq. 1.4 could be helpful.
3 - It is used in multiple occasions that the special interface transition is essentially equivalent to no defect for all N. On the other hand, the boundary special transition has non-trivial anomalous dimensions with the respect to the bulk operators. Is there a simple way to argue for the triviality of the interface with an action similar to 1.4 or 2.2 for the special boundary class?
4 - The folding construction is used a few times in the text. Could one have anticipated eq. 5.37 from 3.34 + the folding argument?
5 - Reference https://inspirehep.net/literature/1837673 computes conformal data for the O(N) conformal interface in the epsilon expansion (for the ordinary and special transitions ). Maybe these results could be mentioned. Perhaps some of the them are useful to compare with?