(Anti-)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory

We exploit the beauty and strength of the symmetry invariant restrictions on the (anti-)chiral superfields to derive the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations in the case of a two (1+1)-dimensional (2D) self-dual chiral bosonic field theory within the framework of augmented (anti-)chiral superfield formalism. Our 2D ordinary theory is generalized onto a (2, 2)-dimensional supermanifold which is parameterized by the superspace variable Z^M = (x^\mu, \theta, \bar\theta) where x^\mu (with \mu = 0, 1) are the ordinary 2D bosonic coordinates and (\theta,\, \bar\theta) are a pair of Grassmannian variables with their standard relationships: \theta^2 = {\bar\theta}^2 =0, \theta\,\bar\theta + \bar\theta\theta = 0. We impose the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral superfields (defined on the (anti-)chiral (2, 1)-dimensional super-submanifolds of the above general (2, 2)-dimensional supermanifold) to derive the above nilpotent symmetries. We do not exploit the mathematical strength of the (dual-)horizontality conditions anywhere in our present investigation. We also discuss the properties of nilpotency, absolute anticommutativity and (anti-)BRST and (anti-)co-BRST symmetry invariance of the Lagrangian density within the framework of our augmented (anti-)chiral superfield formalism. Our observation of the absolute anticommutativity property is a completely novel result in view of the fact that we have considered only the (anti-)chiral superfields in our present endeavor.