SciPost Submission Page
Bootstrapping traceless symmetric O(N) scalars
by Marten Reehorst, Maria Refinetti, Alessandro Vichi
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Marten Reehorst |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202207_00037v1 (pdf) |
| Date submitted: | July 25, 2022, 1:30 p.m. |
| Submitted by: | Marten Reehorst |
| 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 (Referee 2) on 2022-10-6 (Invited Report)
Report
Report #1 by Connor Behan (Referee 1) 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 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
- Duplicated references are [10] = [62], [11] = [58] and [55] = [68].
- The paper frequently switches between "indexes" and "indices".
- 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.
- The last equation on page 31 uses the same dummy index too many times.
- 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.
- The right plot of Fig 19 lists four assumptions but $\Delta_{J^\prime} > 3$ makes less sense than the other three.
- 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.
- On page 25, there is one reference to Fig 18b which should say 19b.
- At the top of page 18, there is a $t^\prime$ which should be a subscript of $\Delta$.
- 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,
- Other missing plurals are "in many case" starting section 1.2 and "the above model have been" in section 1.3.