Bootstrapping traceless symmetric $O(N)$ scalars

We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors O(N) O(N) with two indices t_{ij} display="inline">tij . obtain upper bounds on operator dimensions for all the relevant representations and several values N display="inline">N discover families kinks, which do not correspond any known model we discuss possible candidates. then specialize case N=4 display="inline">N=4 , has been conjectured describe a phase transition in antiferromagnetic real projective ARP^{3} display="inline">ARP3 Lattice simulations provide strong evidence existence second order transition, while an effective field theory approach does predict fixed point. identify set assumptions that constrain closed region overlapping lattice prediction. The is still present after pushing numerics single correlator or when considering mixed system involving t display="inline">t lowest dimension scalar singlet.