Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-01-19
Phys.Rev.D73:106001,2006
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, references added
Scientific paper
10.1103/PhysRevD.73.106001
In a previous paper (hep-th/0510080) the effective Landau-Lifshitz (LL) Lagrangians in the SU(2) sector coming from string theory and gauge theory have been found to three loops in the effective expansion parameter $\tilde\lambda=\lambda/J^2$. In this paper we continue this study and find the effective Landau-Lifshitz Lagrangians to four loops. We extend to four-loops $\tilde\lambda^4$ the computations of 1/J and $1/J^2$ corrections to BMN energies done in hep-th/0510080 to three-loops. We compare these corrections obtained from quantum ``gauge-theory'' LL action with the corrections obtained from the conjectured Bethe ansatz for the long range spin chain representing perturbative {large $N$} $\NN=4$ Super Yang-Mills in the SU(2) sector and find perfect matching to four loops $\tilde\lambda^4$. We compare also the 1/J and $1/J^2$ corrections obtained from quantum ``string-theory'' LL action with those obtained from the "quantum string" Bethe ansatz and again find perfect matching to four-loops.
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