Nilpotent Symmetries and Curci-Ferrari Type Restrictions in 2D Non-Abelian Gauge Theory: Superfield Approach

Abstract

We derive the off-shell nilpotent symmetries of the two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci-Ferrari (CF) type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen (2, 2)-dimensional supermanifold. The latter is parameterized by the superspace coordinates Z^{M} = (x^{\mu}, \theta, \bar\theta) where x^{\mu } (with \mu = 0,1) are the bosonic coordinates and a pair of Grassmannian variables (\theta, \bar\theta) obey the relationships: \theta^{2} = \bar\theta^{2} = 0, \theta\bar\theta + \bar\theta\theta = 0.