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Bootstrapping traceless symmetric $O(N)$ scalars
by Marten Reehorst, Maria Refinetti, Alessandro Vichi
Submission summary
| Authors (as Contributors): | Marten Reehorst |
| Submission information | |
|---|---|
| Preprint link: | scipost_202207_00037v2 |
| Date accepted: | 2023-01-10 |
| Date submitted: | 2022-11-23 16:24 |
| 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.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Author comments upon resubmission
List of changes
Changed the example barion-like state and added footnote 5.