Bootstrapping traceless symmetric $O(N)$ scalars

Reehorst, Marten; Refinetti, Maria; Vichi, Alessandro

doi:10.21468/SciPostPhys.14.4.068

SciPost Physics

Bootstrapping traceless symmetric $O(N)$ scalars

Marten Reehorst, Maria Refinetti, Alessandro Vichi

SciPost Phys. 14, 068 (2023) · published 12 April 2023

doi: 10.21468/SciPostPhys.14.4.068
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Abstract

We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indices $t_{ij}$. 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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.14.4.068
TI  - Bootstrapping traceless symmetric $O(N)$ scalars
PY  - 2023/04/12
UR  - https://www.scipost.org/SciPostPhys.14.4.068
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 14
IS  - 4
SP  - 068
A1  - Reehorst, Marten
AU  - Refinetti, Maria
AU  - Vichi, Alessandro
AB  - We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indices $t_{ij}$. 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.
ER  -

@Article{10.21468/SciPostPhys.14.4.068,
	title={{Bootstrapping traceless symmetric $O(N)$ scalars}},
	author={Marten Reehorst and Maria Refinetti and Alessandro Vichi},
	journal={SciPost Phys.},
	volume={14},
	pages={068},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.14.4.068},
	url={https://scipost.org/10.21468/SciPostPhys.14.4.068},
}

Cited by 4

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¹ ² Marten Reehorst,
¹ ³ Maria Refinetti,
¹ ⁴ Alessandro Vichi

Funders for the research work leading to this publication