Speaker
Description
We provide a new construction of superfield collinear twist-$2$ operators as infinite-dimensional, irreducible representations of the collinear superconformal algebra in the zero-coupling limit of $\mathcal{N}=1$ supersymmetric Yang-Mills (SYM) theory in a manifestly gauge-invariant and supersymmetric-covariant fashion.This construction makes manifest their mixing and renormalization properties at one loop. We compute their asymptotic renormalization-group improved generating functional in Euclidean superspace and its planar and leading nonplanar large-$N$ expansion. We verify that the leading nonplanar asymptotic RG-improved generating functional matches the structure of logarithm of a functional superdeterminant of the corresponding nonperturbative object arising from the glueball/gluinoball effective action, which it should be asymptotic to at short distances because of the asymptotic freedom. Hence, our large-$N$ computation sets strong ultraviolet asymptotic constraints on the nonperturbative solution of large-$N$ $\mathcal{N} = 1$ SYM theory that may be a pivotal guide for the search of such a solution.
