Generating functional of correlators of twist-$2$ operators in $\mathcal{N} = 1$ SUSY Yang-Mills theory, I

Abstract

The present paper is the first installment where, extending our previous work in pure Yang-Mills (YM) theory, we compute the generating functional of correlators of collinear twist-$2$ operators that enter the components of balanced superfields -- i.e., superfields with an equal number of dotted and undotted indices in their spinor representation -- in $\mathcal{N} = 1$ SUSY SU($N$) YM theory in Minkowskian and Euclidean space-time, in the conformal limit and renormalization-group (RG) improved form, and to the leading and next-to-leading order in the large-$N$ expansion. Moreover, we compare our asymptotic RG-improved generating functional to the next-to-leading large-$N$ order with the corresponding nonperturbative object arising from the glueball/gluinoball one-loop effective action, which it should be asymptotic to at short distances because of the asymptotic freedom. Remarkably, we find that both have the structure of the logarithm of a functional superdeterminant. Hence, our large-$N$ computation sets strong ultraviolet asymptotic constraints on the nonperturbative solution of large-$N$ $\mathcal{N} = 1$ SUSY YM theory that may be a pivotal guide for the search of such a solution.