Abstract
The high-energy behavior of the N=4 SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large Nc, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in the first two orders in coupling constant: BFKL intercept and NLO BFKL intercept calculated in Kotikov and Lipatov (2000, 2003, 2004) [1]. As an example of using the Wilson-line OPE, we calculate the coefficient function in front of the pomeron for the correlator of four Z2 currents in the first two orders in perturbation theory.
Highlights
The high-energy scattering in a gauge theory can be described in terms of Wilson lines – infinite gauge factors ordered along the straight lines
For a fast particle scattering off some target, this eikonal phase factor is a Wilson line – an infinite gauge link ordered along the straight line collinear to particle’s velocity nμ:
The main result of the Letter is that the rapidity factorization and high-energy operator expansion in color dipoles works at the NLO level
Summary
The high-energy scattering in a gauge theory can be described in terms of Wilson lines – infinite gauge factors ordered along the straight lines (see e.g. the review [2]). The high-energy behavior of the amplitudes can be studied in the framework of the rapidity evolution of Wilson-line operators forming color dipoles [3,4]. The result of second integration is again the impact factor times color dipole ordered in the direction of target’s velocity with rapidities greater than Y B. Our main goal is the description of the amplitude in the next-to-leading order in perturbation theory, but it is worth noting that the pomeron intercept is known in the limit of large ’t Hooft coupling λ = 4π αs Nc ω(ν) + 1 = j(ν) = 2 − 2 ν2√+ 1. In the rest of the Letter we will do this using the high-energy operator product expansion in Wilson lines [5]
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