Augmented Superfield Approach to Nilpotent Symmetries in Self-Dual Chiral Bosonic Field Theory

Research paper by N. Srinivas, T. Bhanja, R. P. Malik

Indexed on: 11 May '15Published on: 11 May '15Published in: High Energy Physics - Theory


We exploit the beauty and strength of the symmetry invariant restrictions on the 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 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 superfields, defined on the (anti-)chiral (2, 1)-dimensional super-submanifolds of the above {\it general} (2, 2)-dimensional supermanifold, to derive the above nilpotent symmetries. We do not exploit the theoretical strength of (dual-)horizontality conditions {\it anywhere} in our present investigation. We also discuss the properties of nilpotency, absolute anticommutativity and symmetry invariance of the Lagrangian density in our augmented superfield formalism.