Quadratic gauge in 2-form gauge theory by generalized fermionic rigid symmetry transformation

In this work, we extend the scope of rigid fermionic BRST transformations within the framework of Abelian 2-form gauge theory by introducing a finite and field- dependent transformation parameter. This reformulation reveals a significant impact on the exploration of the theory under quadratic gauge conditions. By adopting this generalized BRST structure, we establish a direct correspondence between generating functionals of distinct effective models. The transformations, defined via varying finite parameters, provide a systematic mechanism to relate different effective formulations, thereby offering deeper insights into the gauge structure of the Abelian 2-form theory.