Bootstrapping traceless symmetric $O(N)$ scalars

TL;DR

This paper employs numerical bootstrap methods to analyze $O(N)$ symmetric traceless tensors, revealing new bounds on operator dimensions, discovering novel kinks, and providing insights into phase transitions in the $N=4$ case related to the ARP$^{3}$ model.

Contribution

It introduces new bootstrap bounds for $O(N)$ traceless symmetric tensors and identifies unexplored kinks, offering potential insights into phase transitions in related models.

Findings

Discovery of several families of kinks not matching known models

Strong lattice evidence for a second order phase transition at N=4

Operator dimension bounds overlapping with lattice predictions

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.