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Living on the walls of super-QCD
by Vladimir Bashmakov, Francesco Benini, Sergio Benvenuti, Matteo Bertolini
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Submission summary
| Authors (as registered SciPost users): | Francesco Benini · Matteo Bertolini |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/1812.04645v2 (pdf) |
| Date submitted: | 2019-01-17 01:00 |
| Submitted by: | Benini, Francesco |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study BPS domain walls in four-dimensional $\mathcal{N}=1$ massive SQCD with gauge group $SU(N)$ and $F<N$ flavors. We propose a class of three-dimensional Chern-Simons-matter theories to describe the effective dynamics on the walls. Our proposal passes several checks, including the exact matching between its vacua and the solutions to the four-dimensional BPS domain wall equations, that we solve in the small mass regime. As the flavor mass is varied, domain walls undergo a second-order phase transition, where multiple vacua coalesce into a single one. For special values of the parameters, the phase transition exhibits supersymmetry enhancement. Our proposal includes and extends previous results in the literature, providing a complete picture of BPS domain walls for $F<N$ massive SQCD. A similar picture holds also for SQCD with gauge group $Sp(N)$ and $F < N+1$ flavors.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2019-2-18 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1812.04645v2, delivered 2019-02-17, doi: 10.21468/SciPost.Report.834
Strengths
1) The paper contains an independent analysis from 3d and 4d perspectives that provides non-trivial cross-checks
2) It supplements recent results on 3d N=1 IR dualities with a natural 4d embedding
3) Clarity of presentation.
Weaknesses
It is not entirely clear if the 3d semi-classical analysis of vacua is complete.
Report
In this nicely written paper the authors study the low-energy dynamics on half-BPS domain walls in four-dimensional N=1 massive SQCD with gauge group SU(N) and F<N flavors. The Sp(N) case is also discussed. They propose that the low-energy domain wall theory is a specific 3d N=1 Chern-Simons matter theory, which is a natural generalisation of previous proposals for the domain wall theories on half-BPS domain walls in pure SYM theory. The authors show that their proposal passes a number of non-trivial checks. Most notably, it obeys N=1 infrared dualities precisely as expected from the 4d dynamics and reduces to the expected CS theory at large 4d flavor mass. The analysis of vacua for negative 3d flavor masses is more intricate. A detailed semi-classical analysis of BPS domain wall solutions in the massive 4d SQCD theory in the regime of small flavor mass provides compelling evidence that supports the vacuum structure obtained from the analysis of the proposed 3d theory on the domain walls.
The paper is written clearly with succinct review sections that help the presentation. I did not spot any worrying presentation issues. A single minor typo that I spotted is a missing \epsilon in the second equation in (2.12).
The only issue I would like to bring up on a technical level is the following. The proposed 3d CS-matter theory includes a classically massless scalar multiplet $\Phi$ in the adjoint representation. It is known that quantum effects make this multiplet massive and the authors use this fact to integrate out $\Phi$. Their 3d analysis is performed exclusively in the 3d N=1 CS-matter theory with the adjoint scalar multiplet integrated-out. It is also known that the mass of the multiplet $\Phi$ can be made parametrically small when the rank N of the bulk gauge group is large. Therefore, it is not very clear to me how strongly one can justify the semi-classical integration of $\Phi$. Could the full quantum dynamics of $\Phi$ affect significantly any of the aspects of the 3d analysis performed by the authors, e.g. the analysis of the vacua performed in section 4.1? Could there be potential effects that are missed by (4.3), which focuses on classically marginal and relevant couplings? In principal, higher order superpotential terms could be relevant if there are large anomalous dimensions. It is mentioned in the second sentence of page 13 that ''Higher order terms in W are expected to be irrelevant at the point m = 0''. However, some of the most intricate results are obtained for m non-vanishing. If there are potential alternatives to their analysis the authors should indicate them. If there are no alternatives and the authors believe that their arguments are robust it would be useful to mention relevant arguments explicitly.
The paper contains a number of important results with several non-trivial cross-checks. These results will be useful in future explorations of 3d non-supersymmetric QFTs and their connections to 4d physics. Besides the embedding of recently discussed 3d N=1 infrared dualities in 4d QFT the authors present interesting observations on supersymmetry enhancement and perform computations both in SU(N) and Sp(N) SQCD. For these reasons I believe the paper deserves to be published, but before my final recommendation I would like the authors to address the question I raised above.
Requested changes
I would like the authors to address the question I raised in my report.
Report #1 by Anonymous (Referee 3) on 2019-2-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1812.04645v2, delivered 2019-02-08, doi: 10.21468/SciPost.Report.818
Strengths
see report
Weaknesses
see report
Report
The paper "Living on the walls of super-QCD", written by four authors whose surn
ame starts with B, concerns the 3d theory that lives on the walls of SQCD with F
<N. The theory admits an interesting structure.
For large and positive quark mass the 3d was found by Acharya-Vafa long time ago
. For small quark mass the authors find an interesting Grassmanian coupled to a
TFT. There is a phase transition in between.
The paper is very interesting and contains nice physics about the interplay betw
een 4d bulk physics and 3d worldvolume domain walls physics.
The paper is also nicely written.
I therefore recommend its publication.
Requested changes
n/a