On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory

Abstract

We study the the high spin expansion of the anomalous dimension for long operators belonging to the $sl(2)$ sector of $\mathcal{N}=4$ SYM. Keeping the ratio $j$ between the twist and the logarithm of the spin fixed, the anomalous dimensions expand as $\gamma =f(g,j)\ln s+f^{(0)}(g,j)+O(1/\ln s)$. This particular double scaling limit is efficiently described, up to the desired accuracy $O(\ln s^0)$, in terms of linear integral equations. By using them, we are able to evaluate both at weak and strong coupling the sub-leading scaling function $f^{(0)}(g,j)$ as series in $j$, up to the order $j^5$. Thanks to these results, the possible extension of the liaison with the O(6) non-linear sigma model may be tackled on a solid ground.

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Cited by in corpus (3)

• Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Beyond cusp anomalous dimension from integrability in SYM${}_4$