Augmented Superfield Approach To Exact Nilpotent Symmetries For Matter Fields In Non-Abelian Theory

We derive the nilpotent (anti-) BRST symmetry transformations for the Dirac (matter) fields of an interacting four $(3+1)$-dimensional 1-form non-Abelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4, 2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates $x^\mu$ (with $\mu = 0,1,2,3)$ and a couple of Grassmannian variables $\theta $ and $\bar{\theta}$. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five ($4, 1)$-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4, 2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed in the framework of augmented superfield formalism