On the highest transcendentality in N=4 SUSY

By Anatoly V. Kotikov, L. Lipatov. 2006

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Abstract We investigate the Eden–Staudacher equation for the anomalous dimension of the twist-2 operators at the large spin s in the N = 4 super-symmetric gauge theory. This equation is reduced to a set of linear algebraic equations with the kernel calculated analytically. We prove that in perturbation theory the anomalous dimension is a sum of products of the Euler functions ζ ( k ) having the property of the maximal transcendentality with the coefficients being integer numbers. The radius of convergency of the perturbation theory is found. It is shown, that at g = ∞ the kernel has an essential singularity. The analytic properties of the solution of the Eden–Staudacher equation are investigated. In particular for the case of the strong coupling constant the solution has an essential singularity on the second sheet of the variable j appearing in its Laplace transformation. Similar results are derived also for the Beisert–Eden–Staudacher equation which includes the contribution from the phase related to the crossing symmetry of the underlying S -matrix. We show, that its singular solution at large coupling constants reproduces the anomalous dimension predicted from the string side of the AdS/CFT correspondence.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/28834e52edd0073ac2eec748248666d6b1d23c32

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Citations in the corpus

Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT (2006, result): “Checking this universality was one of our motivations in view of recent remarkable results [19, 18, 20, 21] (see also [22, 23]).”
Four loop twist two, BFKL, wrapping and strings (2008, methodology): “Their anomalous dimensions have been computed perturbatively (in QCD) up to 3 loops [30] and using the maximum transcendentality conjecture [31] for N = 4 SYM the corresponding answer in N = 4 SYM has been extracted [32, 33, 34 ].”
Dressing and wrapping (2007, result): “urning this around, we might say that the wrapping terms should be subleading in the large spin limit. This is reassuring, in particular since by now it appears that the scaling function matches well [44] the known string theory results [45]. Furthermore, the analytic structure of the dressing phase”