Light-cone continuous-spin field in AdS space

We develop further the general light-cone gauge approach in AdS space and apply it for studying continuous-spin field. For such field, we find light-cone gauge Lagrangian and realization of relativistic symmetries. We find a simple realization of spin operators entering our approach. Generalization of our results to the gauge invariant Lagrangian formulation is also described. We conjecture that, in the framework of AdS/CFT, the continuous-spin AdS field is dual to light-ray conformal operator. For some particular cases, our continuous-spin field leads to reducible models. We note two reducible models. The first model consists of massive scalar, massless vector, and partial continuous-spin field involving fields of all spins greater than one, while the second model consists of massive vector, massless spin-2 field, and partial continuous-spin field involving all fields of spins greater than two.