Christ–Lee Model: Augmented Supervariable Approach

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.

Christ–Lee Model: (Anti-)chiral Supervariable Approach to BRST Formalism

“…which imply that the generalized version of super Lagrangians remains quasi-invariant (i.e., up to a total time derivative) under the translational generators ð∂ ϑ , ∂ ϑ Þ within the scope of ACSA which are consistent with Equation (10). Now, we capture the (anti-)co-BRST invariance of the Lagrangian (7) within the scope of (anti-)chiral supervariable approach.…”

“…The latter fermionic-type symmetry transformations are valid for any D-dimensional p-form (p = 1, 2, 3, ⋯) gauge theories in D = 2p dimensions of spacetime. We point out that there are some specific systems such as rigid rotor and Christ-Lee (CL) model in one dimension (1D) that respect the (anti-)co-BRST transformations along with the (anti-)BRST transformations [7][8][9][10].…”

“…Within the framework of BRST formalism, the CL model respects six independent continuous symmetries (i.e., BRST, anti-BRST, co-BRST, anti-co-BRST, ghost-scale, and bosonic symmetries) (see, e.g., [9] for detail). The BT-superfield formalism has been applied to obtain the absolutely anticommuting and offshell nilpotent (anti-)BRST as well as (anti-)co-BRST symmetry transformations where the techniques of celebrated horizontality condition (HC) and dual horizontality condition have been used [10], respectively.…”

Christ-Lee Model: (Anti-)Chiral Supervariable Approach to BRST Formalism

“…The latter symmetry transformations are true for any D-dimensional p-form (p = 1, 2, 3, ...) gauge theories in D = 2p dimensions of spacetime. We point out that there are some specific systems such as rigid rotor and Christ-Lee (CL) model in one-dimension that respect the (anti-)co-BRST transformations in addition to the (anti-)BRST transformations [7][8][9][10].…”

“…[9] for detail). The BT-superfield formalism has been applied to obtain the offshell nilpotent and absolutely anticommuting (anti-)BRST and (anti-)co-BRST symmetry transformations where the technique of celebrated horizontality condition (HC) and dual horizontality condition have been used [10].…”