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Bootstrapping traceless symmetric $O(N)$ scalars
by Marten Reehorst, Maria Refinetti, Alessandro Vichi
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Submission summary
| Authors (as registered SciPost users): | Marten Reehorst |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2012.08533v2 (pdf) |
| Date submitted: | 2022-11-04 14:52 |
| Submitted by: | Reehorst, Marten |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indexes $t_{ij}$. We obtain upper bounds on operator dimensions for all the relevant representations and several values of $N$. We discover several families of kinks, which do not correspond to any known model and we discuss possible candidates. We then specialize to the case $N=4$, which has been conjectured to describe a phase transition in the antiferromagnetic real projective model ARP$^{3}$. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to a closed region overlapping with the lattice prediction. The region is still present after pushing the numerics in the single correlator case or when considering a mixed system involving $t$ and the lowest dimension scalar singlet.
Author comments upon resubmission
List of changes
Fixed all the requested typo changes suggested by the referees. Fixed the imprecision where $\phi$ was considered to transform in the adjoint representation in some comments made in the paper in section 1.3. Now the whole section consistently refers to $\phi$ transforming in the fundamental representation.
Current status:
Reports on this Submission
Report #1 by Connor Behan (Referee 1) on 2022-11-5 (Invited Report)
Report
The authors have done a good job with recent changes and it is now much harder to find typos in the paper. I think it should proceed to publication.
Marco Serone on 2022-11-08 [id 2997]
The authors fixed most typos, but unfortunately some confusion is still left in section 1.3. In eq.(4) and in text below eqs.(4) and (8), \phi^a_i should be replaced by \phi_i^\alpha. The baryon-like states B_{ijk} reported in the text after eq.(8) are not gauge invariant, as the tensor product of three SO(M) fundamentals does not contain a SO(M) singlet. The paper can be published after fixing these left-over typos.
Anonymous on 2022-11-17 [id 3037]
(in reply to Marco Serone on 2022-11-08 [id 2997])Thank you very much for your feedback.
I am not sure I understand "as the tensor product of three SO(M) fundamentals does not contain a SO(M) singlet". I think I wasn't clear when I gave the example that the specific example was for the case of SO(3) and that for SO(M) it would instead have M fields. I now clarified this in the paper as well as the fact that this is SO(3) invariant but not O(3) invariant (but our bootstrap setup does not differentiate between these). In this case the tensor product of three SO(3) fundamentals does contain an SO(3) singlet exactly the one given by contracting with the epsilon tensor. Do you agree or am I missing something? Are you happy with the reformulation (see attached file, truncated to the first 15 pages due to size limit)?
Attachment:
Resubmission_V3_FirstPages.pdf