Holographic constraints on a vector boson

We show that holography poses non-trivial restrictions on various couplings of an interacting field. For a vector boson in the AdS Reissner-Nordstrom background, the dual boundary theory is pathological unless its electromagnetic and gravitational multi-pole moments are constrained. Among others, a generic dipole moment afflicts the dual CFT with superluminal modes, whose remedy bounds the gyromagnetic ratio in a range around the natural value g = 2. We discuss the CFT implications of our results, and argue that similar considerations can shed light on how massive higher-spin fields couple to electromagnetism and gravity.