Colored Spin Systems, BKP Evolution and finite N_c effects

TL;DR

This paper investigates the spectrum of 4-gluon BKP kernels at finite color numbers using toy models, revealing how the spectrum varies with the number of colors and comparing it to the integrable large N_c limit.

Contribution

It introduces solvable toy models for 4-gluon BKP kernels at finite N_c and analyzes their spectral dependence, bridging the gap between finite and large N_c regimes.

Findings

Spectrum depends on the number of colors N_c

Toy models are solvable with group theory methods

Comparison with the large N_c limit shows notable differences

Abstract

Even within the framework of the leading logarithmic approximation the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the planar limit case where the problem becomes integrable. We consider a 4-gluon kernel for a finite number of colors and define some simple toy models for the configuration space dynamics, which are directly solvable with group theoretical methods. Then we study the dependence of the spectrum of these models with respect to the number of colors and make comparisons with the large limit case.