# Bootstrapping traceless symmetric $O(N)$ scalars

### Submission summary

 Authors (as Contributors): Marten Reehorst
Submission information
Date accepted: 2023-01-10
Date submitted: 2022-11-23 16:24
Submitted by: Reehorst, Marten
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Condensed Matter Physics - Theory
• High-Energy Physics - Theory
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:
Accepted in target Journal

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

We made the final changes requested by Marco Serone in section 1.3

### List of changes

Changed the example barion-like state and added footnote 5.