Nilpotent Symmetries of the 4D Abelian 2-Form Gauge Theory: Augmented Superfield Formalism

Research paper by N. Srinivas, A. Shukla, R. P. Malik

Indexed on: 27 Jan '15Published on: 27 Jan '15Published in: High Energy Physics - Theory


We derive the continuous nilpotent symmetries of the four (3 + 1)-dimensional (4D) Abelian 2-form gauge theory by exploiting the geometrical superfield formalism where the (dual-)horizontality conditions are not used anywhere. These nilpotent symmetries are the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST transformations which turn up beautifully due to the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral superfields that are defined on the (4, 1)-dimensional (anti-)chiral super-submanifolds of the general (4, 2)-dimensional supermanifold on which our ordinary 4D theory is generalized. The latter supermanifold is characterized by the superspace coordinate Z^M = (x^\mu, \theta, \bar\theta) where x^\mu (\mu = 0, 1, 2, 3) are the bosonic coordinates and a pair of Grassmannian variables \theta and \bar\theta obey the standard relationships: \theta^2 = \bar\theta^2 = 0, \theta\bar\theta + \bar\theta\theta = 0. We provide the geometrical interpretation for the nilpotency property of the above transformations that are present in the ordinary 4D theory. The derivation of the proper (anti-) co-BRST symmetry transformations is a novel result of our present investigation.