Notes on the Quantization of the Complex Linear Superfield

TL;DR

This paper discusses the quantization process of the complex linear superfield, addressing the infinite ghost tower issue, and extends existing methods by incorporating Lagrange multipliers and analyzing BRST cohomology.

Contribution

It generalizes the Batalin-Vilkovisky quantization technique for complex linear superfields by including Lagrange multipliers and studying the BRST cohomology structure.

Findings

Successfully incorporated Lagrange multipliers into the non-minimal sector.

Analyzed the BRST cohomology to identify the physical subspace.

Performed quantization with background and quantum gauge superfields.

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 characteristic 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.