Exploring $SU(N)$ adjoint correlators in $3d$

Abstract

We use numerical bootstrap techniques to study correlation functions of scalars transforming in the adjoint representation of $SU(N)$ in three dimensions. We obtain upper bounds on operator dimensions for various representations and study their dependence on $N$. We discover new families of kinks, one of which could be related to bosonic QED${}_3$. We then specialize to the cases $N=3,4$, which have been conjectured to describe a phase transition respectively in the ferromagnetic complex projective model $C{P}^2$ and the antiferromagnetic complex projective model $AC{P}^3$. 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 small regions overlapping with the lattice predictions.

41 pages, 10 figures

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• Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid
• CFTs with $U(m)\times U(n)$ Global Symmetry in 3D and the Chiral Phase Transition of QCD
• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions