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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: | scipost_202207_00037v1 (pdf) |
| Date submitted: | 2022-07-25 13:30 |
| 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 a 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.
Current status:
Reports on this Submission
Report 2 by Marco Serone on 2022-10-6 (Invited Report)
Report
Publish after minor corrections are made
Report 1 by Connor Behan on 2022-9-19 (Invited Report)
- Cite as: Connor Behan, Report on arXiv:scipost_202207_00037v1, delivered 2022-09-19, doi: 10.21468/SciPost.Report.5712
Report
This work studies 3D critical points where the order parameter is a traceless symmetric tensor. This is the type of operator which led to a drastic shrinking of numerical bootstrap islands for the O(2) and O(3) models two years ago. For the present study, the authors shift their attention to the ARP3 model and other conjectured fixed points which are still associated with large error bars in the literature. A systematic search leads to an island which favours lattice predictions over those of the epsilon expansion.
This paper also communicates valuable lessons about how numerical bootstrap plots should be interpreted. Appendix C gives precise conditions which are required for the tensor bounds of one orthogonal group to differ from the vector bounds of another. There is also a nice discussion in section 3 showing that certain gaps may be imposed without loss of generality while still improving the bounds. The authors use this observation to find a new family of kinks, rule out an old family as unphysical and discuss future prospects involving the navigator method.
I have only good things to say about this paper's results but it seems to contain a number of typographical oversights which are listed below. I think at least a subset of them should be fixed before this proceeds to publication.
Requested changes
1. Duplicated references are [10] = [62], [11] = [58] and [55] = [68].
2. The paper frequently switches between "indexes" and "indices".
3. It is often not consistent which letters are caligraphic. This includes O on page 31, N on page 32 and K on page 33. Similarly $Z_2$ on pages 16 and 27 should have its font changed.
4. The last equation on page 31 uses the same dummy index too many times.
5. The caption of Fig 18 neglects to mention that the green line comes from imposing that $t$ is the lightest symmetric tensor. Similarly, the caption of Fig 16 lists assumptions but it should mention that these were used for the dark region only.
6. The right plot of Fig 19 lists four assumptions but $\Delta_{J^\prime} > 3$ makes less sense than the other three.
7. Appendix A refers to "the previous section" instead of section 2 while the beginning of section 2.3 refers to section 4.3 instead of itself.
8. On page 25, there is one reference to Fig 18b which should say 19b.
9. At the top of page 18, there is a $t^\prime$ which should be a subscript of $\Delta$.
10. Other changes to make are "a traceless symmetric tensors" -> "a traceless symmetric tensor" in the abstract, "the the O(2)" -> "the O(2)" on page 4, "the lattices size" -> "the lattice's size" on page 5, "will be denote by" -> "will be denoted by" on page 8, "due to this methods" -> "due to this method's" on page 19 and "simulation support" -> "simulations support" on page 25,
11. Other missing plurals are "in many case" starting section 1.2 and "the above model have been" in section 1.3.