BRST-BV approach to fields in Poincaré patch of AdS

We use the Poincare parametrization of AdS space to develop a general BRST-BV approach for free fields. A general expression for the BRST-BV Lagrangian of fields with arbitrary masses and symmetry types is obtained. We apply this general framework to study totally symmetric massless, massive, and partially-massless fields with arbitrary integer spin and a continuous-spin field. For these fields, the constrained and unconstrained BRST-BV formulations are developed. We investigate both irreducible and reducible fields. In addition, we demonstrate the matching between the obtained BRST-BV Lagrangian and the metric-like Lagrangian formulated in terms of the modified de Donder derivative. Finally, a realization of AdS space symmetries is obtained within the space of fields and antifields entering the BRST-BV formulation. Modulo the choice of the Poincare parametrization of AdS space, the Lagrangian and the entire approach are manifestly Lorentz invariant.