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 anticommuting (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 $$\theta $$ and $$\bar{\theta }$$ (with $$\theta ^2 = \bar{\theta }^2 = 0$$ and $$\theta \bar{\theta }+ \bar{\theta }\theta = 0$$). The dynamics of this system is such that, instead of the full (2, 2)-dimensional superspace coordinates $$(x^\mu , \theta , \bar{\theta }),$$ we require only the specific (1, 2)-dimensional super-subspace variables $$(t, \theta , \bar{\theta })$$ 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 new ingredients of our present endeavor where we have exploited the augmented version of the superfield approach to the BRST formalism