# Christ-Lee Model: Augmented Supervariable Approach

## TL;DR

This paper develops a comprehensive supervariable approach to derive and geometrically interpret the full set of (anti-)BRST and (anti-)co-BRST symmetries for the Christ-Lee gauge-invariant model, highlighting their invariance and conserved charges.

## Contribution

It introduces an augmented supervariable framework to systematically derive and interpret all off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetries for the Christ-Lee model.

## Key findings

- Complete set of (anti-)BRST and (anti-)co-BRST transformations derived.
- Geometrical origin of symmetries explained via supervariables.
- Invariance of the Lagrangian under these symmetries demonstrated.

## Abstract

We derive the complete set of off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations for the gauge-invariant Christ-Lee model by exploiting the celebrated (dual-)horizontality conditions together with the gauge-invariant and (anti-)co-BRST invariant restrictions within the framework of geometrical "augmented" supervariable approach to BRST formalism. We show the (anti-) BRST and (anti-)co-BRST invariances of the Lagrangian in the context of supervariable approach. We also provide the geometrical origin and capture the key properties associated with the (anti-)BRST and (anti-)co-BRST symmetry transformations (and corresponding conserved charges) in terms of the supervariables and Grassmannian translational generators.