Eur. Phys. J. C (2016) 76: 230
https://doi.org/10.1140/epjc/s10052-016-4046-4

Regular Article - Theoretical Physics

On Hermitian separability of the next-to-leading order BFKL kernel for the adjoint representation of the gauge group in the planar SYM

¹ Budker Institute of Nuclear Physics of SD RAS, Novosibirsk, 630090, Russia
² Novosibirsk State University, Novosibirsk, 630090, Russia
³ Dipartimento di Fisica, Istituto Nazionale di Fisica Nucleare Gruppo collegato di Cosenza, Università della Calabria, Arcavacata di Rende, 87036, Cosenza, Italy

^* e-mail: roberto.fiore@cs.infn.it

Received: 5 March 2016
Accepted: 29 March 2016
Published online: 26 April 2016

Abstract

We analyze a modification of the BFKL kernel for the adjoint representation of the color group in the maximally supersymmetric () Yang–Mills theory in the limit of a large number of colors, related to the modification of the eigenvalues of the kernel suggested by Bondarenko and Prygarin in order to obtain Hermitian separability of the eigenvalues. We restore the modified kernel in the momentum space. It turns out that the modification is related only to the real part of the kernel and that the correction to the kernel cannot be presented by a single analytic function in the entire momentum region, which contradicts the known properties of the kernel.