Narrow Results

In the framework of superfield formalism, we demonstrate the existence of a new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the BRST invariant Lagrangian density of a self-interacting two (1+1)-dimensional (2D) non-Abelian gauge theory (having no interaction with matter fields). The local and nilpotent Noether conserved charges corresponding to the above continuous symmetries find their geometrical interpretation as the translation generators along the odd (Grassmannian) directions of the four (2+2)-dimensional compact supermanifold.

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 parametrized by the superspace coordinates $Z^M=(x^{\mu },𝜃,\overline{𝜃})$ where $x^{\mu }$ (with $\mu =0,1$) are the bosonic coordinates and a pair of Grassmannian variables $(𝜃,\overline{𝜃})$ obey the relationships: ${𝜃}^2={\overline{𝜃}}^2=0$, $𝜃\overline{𝜃}+\overline{𝜃}𝜃=0$. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.