First-principles derivation of the AdS/CFT Y-systems

Abstract

We provide a first-principles, perturbative derivation of the AdS5/CFT4 Y-system that has been proposed to solve the spectrum problem of N=4 SYM. The proof relies on the computation of quantum effects in the fusion of some loop operators, namely the transfer matrices. More precisely we show that the leading quantum corrections in the fusion of transfer matrices induce the correct shifts of the spectral parameter in the T-system. As intermediate steps we study UV divergences in line operators up to first order and compute the fusion of line operators up to second order for the pure spinor string in AdS5xS5. We also argue that the derivation can be easily extended to other integrable models, some of which describe string theory on AdS4, AdS3 and AdS2 spacetimes.

45 pages, 5 figures; v2: minor additions, JHEP version

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Cited by in corpus (15)

• Solving the AdS/CFT Y-system
• Integrability of the AdS_5 x S^5 superstring and its deformations
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Introduction to the thermodynamic Bethe ansatz
• Superspace conformal field theory
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• On the equivalence theorem for integrable systems
• $Ad{S}_5\times S^5$ supergravity vertex operators
• Integrable theories and generalized graded Maillet algebras
• The r-matrix of the Alday-Arutyunov-Frolov model
• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators
• AdS pure spinor superstring in constant backgrounds
• Master symmetry in the $Ad{S}_5\times S^5$ pure spinor string
• Vertex operators for the plane wave pure spinor string
• Quantum corrections to $Ad{S}_5\times S^5$ left-invariant superstring current algebra