The generalised scaling function: a systematic study

Understand

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.