Abstract
We compute, to the lowest perturbative order in SU(N) Yang-Mills theory, n-point correlators in the coordinate and momentum representation of the gauge-invariant twist-2 operators with maximal spin along the p+ direction, both in Minkowskian and — by analytic continuation — Euclidean space-time. We also construct the corresponding generating functionals. Remarkably, they have the structure of the logarithm of a functional determinant of the identity plus a term involving the effective propagators that act on the appropriate source fields.
Highlights
Introduction and physics motivationsIn the present paper we compute, to the lowest perturbative order in SU(N ) Yang-Mills (YM) theory, n-point connected correlators, G(cnon)f(x1, . . . , xn), in the coordinate representation of the gauge-invariant twist-2 operators with maximal spin along the p+ direction, both in Minkowskian and — by analytic continuation — Euclidean space-time.our computation matches and extends the previous lowest-order perturbative computation of 2- and 3-point gluonic correlators of twist-2 operators in N = 4 SUSY YM theory [1], by including the unbalanced1 operators with collinear twist 2 in pure YM theory and, most importantly, by calculating all the n-point correlators in the balanced and unbalanced sectors separately, and the 3-point correlators in the mixed sector as well.Our physics motivation is threefold
We construct the corresponding generating functionals. They have the structure of the logarithm of a functional determinant of the identity plus a term involving the effective propagators that act on the appropriate source fields
Our computation is preliminary to work out the ultraviolet (UV) asymptotics [4, 5] — based on the renormalization-group (RG) improvement of perturbation theory — of the above Euclidean n-point correlators
Summary
In the present paper we compute, to the lowest perturbative order in SU(N ) Yang-Mills (YM) theory, n-point connected correlators, G(cnon)f(x1, . . . , xn), in the coordinate representation of the gauge-invariant twist-2 operators with maximal spin along the p+ direction, both in Minkowskian and — by analytic continuation — Euclidean space-time. Our computation is an essential ingredient to test the prediction in section 3 of [6] that, by fundamental principles of the large-N ’t Hooft expansion, the generating functional of the nonperturbative leading nonplanar contributions to the aforementioned Euclidean correlators must have the structure of the logarithm of a functional determinant [6] that sums the glueball one-loop diagrams. As an intermediate step for the program above, we construct the generating functionals of the aforementioned lowest-order n-point correlators. They have the structure of the logarithm of a functional determinant of the identity plus a term involving the effective propagators that act on the appropriate source fields. The generating functionals allow us to compute straightforwardly the n-point correlators in the momentum representation, whose structure is slightly simpler than in the coordinate representation
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