FLPR Model: Supervariable approach and a model for Hodge theory

We procure the complete set of (anti-)BRST as well as (anti-)co-BRST symmetry transformations of the Friedberg-Lee-Pang-Ren (FLPR) model within the framework of the supervariable approach. Additionally, we capture the nilpotency and absolute anti-commutativity aspects of these symmetries, along with the invariance of the Lagrangian in terms of translational generators along the Grassmannian directions in the context of the supervariable approach. The anti-commutator of the (anti-)BRST and (anti-)co-BRST symmetries generates a novel bosonic symmetry that retains the ghost part of the Lagrangian invariant. Furthermore, we demonstrate that the system under consideration respects the ghost scale and discrete symmetries, in addition to other symmetries. We show that the generators of all these symmetries cling to the algebra obeyed by the de Rham cohomological operators of differential geometry - thus, the FLPR model presents a toy model for the Hodge theory.