Complete 1loop test of AdS/CFT
Abstract
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 BeisertStaudacher (BS) equations with the HernandezLopez dressing factor where the finite size corrections should reproduce generic one (worldsheet) loop computations around any classical superstring motion in the AdS_{5} × 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 1loop 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 1loop by the sum of charges of fluctuations up to exponentially suppressed contributions in the large angular momentum os the string states. We also point out where precisely we loose the exponential terms in our ab initio analysis. Contrary to all previous studies of finite size corrections, which were limited to simple configurations inside rank 1 subsectors, our treatment is completely general.
 Publication:

Journal of High Energy Physics
 Pub Date:
 April 2008
 DOI:
 10.1088/11266708/2008/04/046
 arXiv:
 arXiv:0709.3487
 Bibcode:
 2008JHEP...04..046G
 Keywords:

 High Energy Physics  Theory
 EPrint:
 12 figures. References added. Couple of words added to abstract