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arXiv · 0808.1886

The generalised scaling function: a systematic study

Davide Fioravanti·Paolo Grinza·Marco Rossi
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Abstract

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

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Davide Fioravanti, Paolo Grinza, Marco Rossi. 2008-08-13. The generalised scaling function: a systematic study. https://doi.org/10.1088/1126-6708/2009/11/037

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