Large spin corrections in ${\cal N}=4$ SYM sl(2): still a linear integral equation

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dc.creatorBombardelli, Diego
dc.creatorFioravanti, Davide
dc.creatorRossi, Marco
dc.date2008-01-31
dc.date2008-06-07
dc.date.accessioned2026-07-07T12:35:56Z
dc.date.available2026-07-07T12:35:56Z
dc.descriptionAnomalous dimension and higher conserved charges in the $sl(2)$ sector of ${\cal N}=4$ SYM for generic spin $s$ and twist $L$ are described by using a novel kind of non-linear integral equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-linear (finite range) integral terms, appearing in the NLIE and in the dimension formula, go to zero as $s\to \infty$. Therefore they can be neglected at least up to the $O(s^0)$ order, thus implying a linear integral equation (LIE) and a linear dimension/charge formula respectively, likewise the 'thermodynamic' (i.e. infinite spin) case. Importantly, these non-linear terms go faster than any inverse logarithm power $(\ln s)^{-n}$, $n>0$, thus extending the linearity validity.
dc.descriptionLatex file, typos corrected, 2 figures, appendix, references and clarifications added
dc.identifierhttps://arxiv.org/abs/0802.0027
dc.identifierhttp://arxiv.org/abs/0802.0027
dc.identifierNucl.Phys.B810:460-490,2009
dc.identifierdoi:10.1016/j.nuclphysb.2008.09.030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217930
dc.subjectHigh Energy Physics - Theory
dc.titleLarge spin corrections in ${\cal N}=4$ SYM sl(2): still a linear integral equation
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