The generalised scaling function: a systematic study
Abstract
We describe a procedure for determining the generalised scaling functions at all the values of the coupling constant. These functions describe the high spin contribution to the anomalous dimension of large twist operators (in the sector) of SYM. At fixed , can be obtained by solving a linear integral equation (or, equivalently, a linear system with an infinite number of equations), whose inhomogeneous term only depends on the solutions at smaller . In other words, the solution can be written in a recursive form and then explicitly worked out in the strong coupling regime. In this regime, we also emphasise the peculiar convergence of different quantities ('masses', related to the ) to the unique mass gap of the nonlinear sigma model and analyse the first next-to-leading order corrections.
Cite
@article{arxiv.0808.1886,
title = {The generalised scaling function: a systematic study},
author = {Davide Fioravanti and Paolo Grinza and Marco Rossi},
journal= {arXiv preprint arXiv:0808.1886},
year = {2011}
}
Comments
Latex version, journal version (with explanatory appendices and more references)