(Anti)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory. (7th March 2017) - Srinivas, N.; Bhanja, T.; Malik, R. P.
Abstract : 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 μ, θ, θ ¯, where x μ (with μ = 0, 1 ) are the ordinary 2D bosonic coordinates and (θ, θ ¯ ) are a pair of Grassmannian variables with their standard relationships: θ 2 = θ ¯ 2 = 0, θ θ ¯ + θ ¯ θ = 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.