Superfield approach to a novel symmetry for non - Abelian gauge theory

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. 1 Introduction For the covariant canonical quantization of the (non-)Abelian gauge theories (endowed with the first-class constraints in the language of Dirac [1,2]), the Becchi-Rouet-Stora-Tyutin (BRST) symmetry [3,4] plays a decisive role where unitarity and gauge invariance are respected together at any arbitrary order of perturbation theory. The BRST formalism is indispensable in the context of modern developments in topological field theories [5-7] and (super)string theories (see, e.g., Ref.[8] and references therein). Its elegant extension to include second-class constraints in its folds [9], its mathematically consistent inclusion in the Batalin-Vilkovisky formalism [10,11], its geometrical interpretation in the framework of superfield formulation [12-16], etc., have elevated the subject of BRST formalism to a level where physical ideas (connected with the gauge theories) and underlying mathematical concepts (related to the differential geometry and cohomology) have merged together in such a fashion that it has become an exciting and interesting area of research for the past many years. Recently, in a set of papers [17-21], a possible connection between the local, continuous and covariant symmetries and their generators on the one hand and the de Rham cohomology operators † of differential geometry on the other hand, has been established in the Lagrangian formulation for the case of 2D free-as well as interacting (non-)Abelian gauge theories. Exploiting these symmetries, the topological nature of 2D free Abelian-and self-interacting non-Abelian gauge theories (having no interaction with matter fields) has been demonstrated [22]. The existence of such kind of local symmetries has also been shown for the physical (3 + 1)-dimensional (4D) free two-form Abelian gauge theory [23]. In the superfield approach [12-16] to BRST formalism for the p-form (p = 1, 2, 3.....) gauge theories, the curvature ((p + 1)-form) tensor is restricted to be flat along the Grass-mannian directions of the (D + 2)-dimensional supermanifold, parametrized by D-number of spacetime (even) coordinates and two Grassmannian (odd) coordinates. This flatness condition, popularly known as horizontality condition ‡ , provides …