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3d Large $N$ Vector Models at the Boundary
by Lorenzo Di Pietro, Edoardo Lauria, Pierluigi Niro
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Submission summary
| Authors (as registered SciPost users): | Lorenzo Di Pietro |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2012.07733v2 (pdf) |
| Date submitted: | Jan. 22, 2021, 9:59 a.m. |
| Submitted by: | Di Pietro, Lorenzo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider a 4d scalar field coupled to large $N$ free or critical $O(N)$ vector models, either bosonic or fermionic, on a 3d boundary. We compute the $\beta$ function of the classically marginal bulk/boundary interaction at the first non-trivial order in the large $N$ expansion and exactly in the coupling. Starting with the free (critical) vector model at weak coupling, we find a fixed point at infinite coupling in which the boundary theory is the critical (free) vector model and the bulk decouples. We show that a strong/weak duality relates one description of the renormalization group flow to another one in which the free and the critical vector models are exchanged. We then consider the theory with an additional Maxwell field in the bulk, which also gives decoupling limits with gauged vector models on the boundary.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2021-7-2 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2012.07733v2, delivered 2021-07-02, doi: 10.21468/SciPost.Report.3171
Strengths
Weaknesses
Report
Without hesitation, I recommend publication.
Requested changes
There were a couple of minor points:
In the introduction $\lambda$ is introduced without stating that it is the gauge coupling.
I lost the thread of the argument in the first bullet point on p 15. The authors state ``the operators $\Phi$ vanishes in the limit, as expected for a decoupled bulk free scalar with Neumann boundary condition''. Naively, I would want $\partial_\perp \Phi$ on the boundary to vanish for Neumann, and so I was not sure what was being said. It might help to reference some equations earlier in the draft, (2.24) and (2.25) for example.
Report #1 by Anonymous (Referee 1) on 2021-4-1 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2012.07733v2, delivered 2021-04-01, doi: 10.21468/SciPost.Report.2751
Strengths
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The paper is very clearly written.
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The results match previous results in various limits, so are probably correct.
Weaknesses
- It's a bit disappointing that only the standard non-interacting conformal boundary conditions were found in the theories considered, tho this matches numerical evidence from a previous bootstrap study. The authors mention that generalizing their work to Chern-Simons matter theories could possibly give interacting boundary conditions, which would be very interesting.
Report
Requested changes
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When the authors consider the fermionic theory coupled to a U(1) gauge field, they should keep in mind that the parity anomaly requires that the number of complex 2 component fermions be even. This will not qualitatively change the main results tho.
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In the conclusion the authors say "due to to the presence of matrix-like degrees of freedom in the large N limit". When the number of colors and Chern-Simons level are both simultaneously large, the theory in fact still has vector degrees of freedom, which is in part why it is still believed to be dual to Vasiliev theory (with a parity breaking term).
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The authors consider generalizing their result to Chern-Simons matter theories with many colors. They should also consider adding a Chern-Simons term just to the U(1) gauge field, which is much simpler, and should give different boundary conditions for each integer value of the Chern-Simons level.
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The authors should also address monopole operators, which appear in QED3 in general. How are these operators affected by the 4d bulk theory? Is it clear how they would map across the duality? Similarly, it would be interesting to see how non-local operators like Wilson loops map across the duality.