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arXiv · 0706.3936

On the commuting charges for the highest dimension SU(2) operators in planar ${\cal N}=4$ SYM

Davide Fioravanti·Marco Rossi
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Abstract

We consider the highest anomalous dimension operator in the SU(2) sector of planar ${\cal N}=4$ SYM at all-loop, though neglecting wrapping contributions. In any case, the latter enter the loop expansion only after a precise length-depending order. In the thermodynamic limit we write both a linear integral equation for the Bethe root density and a linear system obeyed by the commuting charges. Consequently, we determine the leading strong coupling contribution to the density and from this an approximation to the leading and sub-leading terms of any charge $Q_r$: it scales as $λ^{1/4-r/2}$, which generalises the Gubser-Klebanov-Polyakov energy law. In the end, we briefly extend these considerations to finite lengths and 'excited' operators by using the idea of a non-linear integral equation.

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Davide Fioravanti, Marco Rossi. 2007-07-13. On the commuting charges for the highest dimension SU(2) operators in planar ${\cal N}=4$ SYM. https://doi.org/10.1088/1126-6708%2F2007%2F08%2F089

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