On Hermitian separability of the next-to-leading order BFKL kernel for the adjoint representation of the gauge group in the planar N=4 N = 4 SYM

2015/12/28 by V. S. Fadin, Roberto Fiore, R. Fiore
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Eigenvalues and eigenvectors #Gauge group #Gauge theory #Group (periodic table) #Hermitian matrix #Kernel (algebra) #Mathematical physics #Mathematics #Order (exchange) #Particle physics theoretical and experimental studies #Physics #Poisson kernel #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #hep-ph #hep-th

paper · pdf · doi:10.1140/epjc/s10052-016-4046-4

arxiv created 2015/12/28 · openalex publication_date 2016/04/26 · arxiv updated 2016/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We analyze a modification of the BFKL kernel for the adjoint representation of the color group in the maximally supersymmetric ( N=4 ) 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.

Citations

• Gluon Regge trajectory in the two-loop approximation
• The dipole form of the BFKL kernel in supersymmetric Yang–Mills theories
• Nonforward color octet BFKL kernel
• N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution
• NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories