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Self-Dual Chiral Boson: Augmented Superfield Approach

We exploit the standard tools and techniques of the augmented version of Bonora-Tonin (BT) superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST and (anti-)co-BRST symmetry transformations for the Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density of a self-dual bosonic system. In the derivation of the full set of the above transformations, we invoke the (dual-)horizontality conditions, (anti-)BRST and (anti-)co-BRST invariant restrictions on the superfields that are defined on the (2, 2)-dimensional supermanifold. The latter is parameterized by the bosonic variable x^μ\,(μ= 0,\, 1) and a pair of Grassmanian variables θand \barθ(with θ^2 = \barθ^2 = 0 and θ\barθ+ \barθθ= 0). The dynamics of this system is such that, instead of the full (2, 2) dimensional superspace coordinates (x^μ, θ, \barθ), we require only the specific (1, 2)-dimensional super-subspace variables (t, θ, \barθ) for its description. This is a novel observation in the context of superfield approach to BRST formalism. The application of the dual-horizontality condition, in the derivation of a set of proper (anti-)co-BRST symmetries, is also one of the new ingredients of our present endeavor where we have exploited the augmented version of superfield formalism which is geometrically very intuitive.