UV asymptotics of the generating functional of 1-loop glueball correlators in large-N Yang-Mills theory

We compute directly from its path-integral definition as a Gaussian integral the generating functional of conformal correlators to the lowest perturbative order of all twist-2 operators with maximal spin along the light-cone direction in SU(N) Yang-Mills theory. Moreover, by means of a careful choice of the renormalization scheme, we lift the generating functional of the Euclidean conformal correlators to the generating functional of the corresponding renormalization-group (RG) improved correlators that inherits the very same structure of the logarithm of a functional determinant. For large-N the RG-improved generating functional admits a decomposition into planar and leading-order (LO) nonplanar contributions. Remarkably, the RG-improved LO nonplanar generating functional, being asymptotic in the ultraviolet (UV) to the sum of the glueball one-loop diagrams, admits the structure of the logarithm of a functional determinant as well. Hence, the computation above sets strong UV asymptotic constraints on the nonperturbative solution of large-N YM theory and it may be a pivotal guide for the search of such a solution.