Self-dual chiral boson: augmented superfield approach

We exploit the standard tools and techniques of the augmented version of the Bonora-Tonin superfield formalism to derive the off-shell nilpotent and absolutely anti-commuting (anti-) Becchi-Rouet-Stora-Tyutin (BRST) and (anti-) co-BRST symmetry transformations for the BRST-invariant Lagrangian density of a self-dual bosonic system. In the derivation of the full set of the above symmetry transformations, we invoke the (dual-) horizontality conditions, and (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(mu) (mu = 0, 1) and a pair of Grassmannian variables 0 and (0) over bar (with 0(2) = (0) over bar (2) = 0 and 0 (0) over bar + (0) over bar0 = 0). The dynamics of this system is such that, instead of the full (2, 2)-dimensional superspace coordinates (x(mu),0, (0) over bar), we require only the specific (1, 2)-dimensional super-subspace variables (t,theta,(theta) over bar) for its description. This is a novel observation in the context of the superfield approach to the 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 newingredients of our present endeavor where we have exploited the augmented version of the superfield approach to the BRST formalism.