Generating functional of correlators of twist-2 operators in $$\mathscr {N} = 1$$ 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 $$\mathscr {N} = 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> 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 $$\mathscr {N} = 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> SUSY YM theory that may be a pivotal guide for the search of such a solution.