Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-01-31
Nucl.Phys.B810:460-490,2009
Physics
High Energy Physics
High Energy Physics - Theory
Latex file, typos corrected, 2 figures, appendix, references and clarifications added
Scientific paper
10.1016/j.nuclphysb.2008.09.030
Anomalous 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.
Bombardelli Diego
Fioravanti Davide
Rossi Marco
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