A Bootstrap Study of Confinement in AdS

Yang-Mills theory in AdS$_{4}$ with Dirichlet boundary conditions is expected to undergo a transition as the AdS radius varies, since the boundary data is incompatible with confinement in flat space. Various mechanisms have been proposed for the disappearance of the Dirichlet boundary condition. From the boundary viewpoint, the associated $3d$ CFT is a deformation of a generalised free theory of non-Abelian conserved currents, with the deformation governed by the bulk gauge coupling. We test these scenarios by deriving non-perturbative constraints from the numerical conformal bootstrap of the four-point function of non-Abelian conserved currents. We rule out the scenario in which the boundary current decouples. Bounds on the lightest scalar operators disfavour a bulk Higgs mechanism and instead point to a transition driven by a scalar singlet becoming marginal. We also obtain bounds on other scalar operators and on the current central charge, and we refine character-based techniques incorporating parity and charge-conjugation symmetry to determine the operator spectrum of the $3d$ Generalised Free Vector theory. These results may be of independent interest beyond Yang-Mills theory in AdS.