UV asymptotics of n-point correlators of twist-2 operators in SU(N) Yang-Mills theory
【Abstract】 The generating functional WE[JO] of Euclidean correlators of twist-2 operators in SU(N) Yang-Mills theory admits the ’t Hooft large-N expansion: WE[JO]=WsphereE[JO]+WtorusE[JO]+⋯. Nonperturbatively, WsphereE[JO] is a sum of tree diagrams involving glueball propagators and vertices, while WtorusE[JO] is a sum of glueball one-loop diagrams. Moreover, it has been predicted that WtorusE[JO] 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 WsphereE[JO,λ]∼Wasym sphereE[JO,λ] and WtorusE[JO,λ]∼Wasym torusE[JO,λ] in the coordinate representation as all the coordinates of the correlators are uniformly rescaled by a factor λ→0. The calculation is performed in two steps. First, extending our previous work, we compute—directly from its functional-integral definition as a Gaussian integral—the generating functional of the conformal correlators Wconf[JO]=Wconf sphere[JO]+Wconf torus[JO] to the lowest perturbative order of all the twist-2 operators with maximal spin along the p+ direction, in both Minkowskian and—by analytical continuation—Euclidean spacetimes. Thus, we provide a purely perturbative explanation as to why Wconf[JO] has the structure of the logarithm of a functional determinant. Second, by means of a careful choice of the renormalization scheme that reduces the mixing of the above operators to the multiplicatively renormalizable case to all orders of perturbation theory, we lift the generating functional of the Euclidean conformal correlators WconfE[JO] to the generating functional of the renormalization-group improved correlators WasymE[JO,λ]=Wasym sphereE[JO,λ]+Wasym torusE[JO,λ] that inherits the very same structure of the logarithm of a functional determinant. Remarkably, we verify the above prediction that Wasym torusE[JO,λ]—being asymptotic in the UV to WtorusE[JO,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 Yang-Mills theory, and it may be a pivotal guide for the search of such a solution.
【Author】 Marco Bochicchio, Mauro Papinutto, Francesco Scardino
【Journal】 Physical Review D(IF：4.4) Time：2023-09-20