Exploring SU(N) adjoint correlators in 3d

Authors: Andrea Manenti, Alessandro Vichi Preprint number: UUITP-04/21 Abstract: We use numerical bootstrap techniques to study correlation functions of scalars transforming in the adjoint representation of SU(N). 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=3,4, which has been conjectured to describe a phase transition respectively in the non compact complex projective space NCCP^2 and the antiferromagnetic complex projective model ACP^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.