Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-06-26
JHEP0708:089,2007
Physics
High Energy Physics
High Energy Physics - Theory
Latex file, 20 pages, some typos corrected, some technical details expanded and explained
Scientific paper
10.1088/1126-6708/2007/08/089
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 $\lambda ^{1/4-r/2}$, 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.
Fioravanti Davide
Rossi Marco
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