Complete 1-loop 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 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.

12 figures. References added. Couple of words added to abstract

References in corpus (14)

• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Dressing and Wrapping
• On the Singularities of the Magnon S-matrix
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• Wrapping interactions at strong coupling -- the giant magnon
• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• Strong-coupling expansion of cusp anomaly from quantum superstring
• The Four-Loop Dressing Phase of N=4 SYM
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• World-sheet scattering in AdS_5 x S^5 at two loops
• Constructing the AdS/CFT dressing factor
• Quantum Scattering of Giant Magnons

Cited by in corpus (10)

• The all loop AdS4/CFT3 Bethe ansatz
• The AdS4/CFT3 algebraic curve
• A Generalized Scaling Function for AdS/CFT
• Baxter's Q-operators for supersymmetric spin chains
• Quantum Wrapped Giant Magnon
• Constructing the AdS/CFT dressing factor
• From Characters to Quantum (Super)Spin Chains via Fusion
• Giant magnons in AdS_4/CFT_3: dispersion, quantization and finite--size corrections
• Quantum Stability for the Heisenberg Ferromagnet
• Anomalous dimensions of finite size field strength operators in N=4 SYM