Notes on the quantization of the complex linear superfield

Abstract The quantization of the complex linear superfield requires an infinite tower of ghosts. Using the Batalin–Vilkovisky technique, Grisaru, Van Proeyen, and Zanon have been able to define a correct procedure to construct a gauge-fixed action. We generalize their technique by introducing the Lagrange multipliers into the non-minimal sector and we study the BRST cohomology. We show how the physical subspace is singled out. Finally, we quantize the model in the presence of a background and of a quantum gauge superfield.