Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-09-21
JHEP 0804:046,2008
Physics
High Energy Physics
High Energy Physics - Theory
12 figures. References added. Couple of words added to abstract
Scientific paper
10.1088/1126-6708/2008/04/046
We analyze nested Bethe ansatz (NBA) and the corresponding finite size corrections. We find an integral equation which describes these corrections in a closed form. As an application we considered the conjectured Beisert-Staudacher (BS) equations with the Hernandez-Lopez dressing factor where the finite size corrections should reproduce generic one (worldsheet) loop computations around any classical superstring motion in the AdS_5 x S^5 background with exponential precision in the large angular momentum of the string states. Indeed, we show that our integral equation can be interpreted as a sum over all physical fluctuations and thus prove the complete 1-loop consistency of the BS equations. In other words we demonstrate that any local conserved charge (including the AdS Energy) computed from the BS equations is indeed given at 1-loop by the sum of charges of fluctuations up to exponentially suppressed contributions. Contrary to all previous studies of finite size corrections, which were limited to simple configurations inside rank one subsectors, our treatment is completely general.
Gromov Nikolay
Vieira Pedro
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