Complete 1-loop test of AdS/CFT

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 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.