
TL;DR
This paper provides a comprehensive 1-loop test of the AdS/CFT correspondence by deriving an integral equation for finite size corrections in the Bethe ansatz framework, confirming the consistency of the Beisert-Staudacher equations with string theory calculations.
Contribution
It introduces a closed-form integral equation for finite size corrections in the nested Bethe ansatz and proves the 1-loop consistency of the Beisert-Staudacher equations for general string configurations.
Findings
Integral equation describes finite size corrections in a closed form.
Proves 1-loop consistency of BS equations with string theory.
Shows all local conserved charges match 1-loop fluctuation sums.
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 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…
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