English

The generalised scaling function: a systematic study

High Energy Physics - Theory 2011-02-17 v2 High Energy Physics - Phenomenology

Abstract

We describe a procedure for determining the generalised scaling functions fn(g)f_n(g) 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 sl(2)sl(2) sector) of N=4{\cal N}=4 SYM. At fixed nn, fn(g)f_n(g) 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 nn. 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 fn(g)f_n(g)) to the unique mass gap of the O(6)O(6) nonlinear sigma model and analyse the first next-to-leading order corrections.

Keywords

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)

R2 v1 2026-06-21T11:10:08.207Z