(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 BecchiRouet- 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,(theta) over bar), where x(mu) (with mu = 0,1) are the ordinary 2D bosonic coordinates and (theta,(theta) over bar) are a pair of Grassmannian variables with their standard relationships: (2) = 0, theta(theta) over bar vertical bar (theta) over bar 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 supersubmanifolds 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.