UV asymptotics of n-point correlators of twist-2 operators in SU(N) Yang-Mills theory

The generating functional W[J] of Euclidean correlators of twist-2 operators in SU(N) Yang-Mills theory admits the 't Hooft large-N expansion W[J]=W_{sphere}[J]+W_{torus}[J]. Nonperturbatively, W_{sphere}[J] is a sum of tree diagrams involving glueball propagators and vertices, while W_{torus}[J] is a sum of glueball one-loop diagrams. Moreover, it has been predicted that W_{torus}[J] should admit the structure of the logarithm of a functional determinant summing glueball one-loop diagrams. We work out in a closed form the ultraviolet (UV) asymptotics of W_{sphere}[J,λ]∼W_{asym sphere}[J,λ] and W_{torus}[J,λ]∼W_{asym torus}[J,λ] in the coordinate representation as all the coordinates of the correlators are uniformly rescaled by a factor λ→0. Remarkably, we verify the above prediction that W_{asym torus}[J,λ] -- being asymptotic in the UV to W_{torus}[J,λ] -- 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.