Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-11-16
J.Stat.Mech.0702:P02001,2007
Physics
High Energy Physics
High Energy Physics - Theory
On the 75-th Anniversary of Bethe Ansatz, 37 Pages, Latex file
Scientific paper
10.1088/1742-5468/2007/02/P02001
As the Hubbard energy at half filling is believed to reproduce at strong coupling (part of) the all loop expansion of the dimensions in the SU(2) sector of the planar $ {\cal N}=4$ SYM, we compute an exact non-perturbative expression for it. For this aim, we use the effective and well-known idea in 2D statistical field theory to convert the Bethe Ansatz equations into two coupled non-linear integral equations (NLIEs). We focus our attention on the highest anomalous dimension for fixed bare dimension or length, $L$, analysing the many advantages of this method for extracting exact behaviours varying the length and the 't Hooft coupling, $\lambda$. For instance, we will show that the large $L$ (asymptotic) expansion is exactly reproduced by its analogue in the BDS Bethe Ansatz, though the exact expression clearly differs from the BDS one (by non-analytic terms). Performing the limits on $L$ and $\lambda$ in different orders is also under strict control. Eventually, the precision of numerical integration of the NLIEs is as much impressive as in other easier-looking theories.
Feverati Giovanni
Fioravanti Davide
Grinza Paolo
Rossi Marco
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