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

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• The Bethe-Ansatz for N=4 Super Yang-Mills
• Type IIB superstring action in AdS_5 x S^5 background
• Transcendentality and Crossing
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Bethe Ansatz for Quantum Strings
• How Algebraic Bethe Ansatz works for integrable model
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Classical/quantum integrability in AdS/CFT
• Giant Magnons
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Multi-spin string solutions in AdS_5 x S^5
• The Factorized S-Matrix of CFT/AdS
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
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• Spin chains and string theory
• Stringing Spins and Spinning Strings
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• Spinning strings in AdS_5 x S^5: new integrable system relations
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Quantum Integrable Systems and Elliptic Solutions of Classical Discrete Nonlinear Equations
• New Exactly Solvable Model of Strongly Correlated Electrons Motivated by High T_c Superconductivity
• Finite-size Effects from Giant Magnons
• Quantum corrections to the string Bethe ansatz
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM
• Quantizing three-spin string solution in AdS_5 x S^5
• Dressing and Wrapping
• On Quantum Corrections to Spinning Strings and Bethe Equations
• 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
• Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory
• Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• Integrability and Transcendentality
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Complete Spectrum of Long Operators in N=4 SYM at One Loop
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
• A Universality Test of the Quantum String Bethe Ansatz
• Spinning strings in AdS_5 x S^5: one-loop correction to energy in SL(2) sector
• Strong-coupling expansion of cusp anomaly from quantum superstring
• Stringy sums and corrections to the quantum string Bethe ansatz
• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1)
• Exact expressions for quantum corrections to spinning strings
• How Accurate is the Quantum String Bethe Ansatz?
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• The Four-Loop Dressing Phase of N=4 SYM
• World-sheet scattering in AdS_5 x S^5 at two loops
• Constructing the AdS/CFT dressing factor
• Strings as Multi-Particle States of Quantum Sigma-Models
• Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings
• Exact Solution of an Electronic Model of Superconductivity in 1+1 Dimensions
• Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz
• Double Scaling and Finite Size Corrections in sl(2) Spin Chain
• Reduced sigma-model on AdS_5 x S^5: one-loop scattering amplitudes
• Filtered overlap: speedup, locality, kernel non-normality and Z_A~1
• Bethe ansatz and fluctuations in SU(3) Yang-Mills operators
• Fluctuations and Energy Shifts in the Bethe Ansatz
• Quantum Scattering of Giant Magnons
• On the Scattering Phase for AdS_5 x S^5 Strings
• A note on the Bethe ansatz solution of the supersymmetric t-J model
• Generalized Spin Systems and $\sigma$--Models
• Rational three-spin string duals and non-anomalous finite size effects

Cited by in corpus (71)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• Integrability and the AdS(3)/CFT(2) correspondence
• The all loop AdS4/CFT3 Bethe ansatz
• Tailoring Three-Point Functions and Integrability
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• A Shortcut to the Q-Operator
• The AdS4/CFT3 algebraic curve
• Superuniversality of superdiffusion
• A Generalized Scaling Function for AdS/CFT
• Baxter's Q-operators for supersymmetric spin chains
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Analytic Solution of Bremsstrahlung TBA
• The Dressing Factor and Crossing Equations
• Tailoring Three-Point Functions and Integrability III. Classical Tunneling
• Superstrings in AdS(2)xS(2)xT(6)
• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• Worldsheet spectrum in AdS(4)/CFT(3) correspondence
• Y-system and Quasi-Classical Strings
• Baxter's Q-operators and operatorial Backlund flow for quantum (super)-spin chains
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• Wronskian Solution for AdS/CFT Y-system
• Quantum Wrapped Giant Magnon
• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• Constructing the AdS/CFT dressing factor
• Fast analytic solver of rational Bethe equations
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories
• From Characters to Quantum (Super)Spin Chains via Fusion
• Quantum integrability and functional equations
• The full Quantum Spectral Curve for $Ad{S}_4/CF{T}_3$
• Deeper Look into Short Strings
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• Y-system and beta-deformed N=4 Super-Yang-Mills
• Giant magnons in AdS_4/CFT_3: dispersion, quantization and finite--size corrections
• $Ad{S}_3/CF{T}_2$, finite-gap equations and massless modes
• Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve
• Twisted Bethe equations from a twisted S-matrix
• Separation of variables and scalar products at any rank
• Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)
• A tree-level 3-point function in the su(3)-sector of planar N=4 SYM
• Superstrings on AdS_4 x CP^3 from Supergravity
• Exact computation of one-loop correction to energy of pulsating strings in AdS_5 x S^5
• Correlation functions of magnon and spike
• Quantum Stability for the Heisenberg Ferromagnet
• Scattering in AdS(2)/CFT(1) and the BES Phase
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• A review of the AdS/CFT Quantum Spectral Curve
• First-principles derivation of the AdS/CFT Y-systems
• Spiky strings in the SL(2) Bethe Ansatz
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• Quantum dispersion relations for excitations of long folded spinning superstring in AdS_5 x S^5
• Spiky strings in Bethe Ansatz at strong coupling
• On the Fermionic Frequencies of Circular Strings
• Toy models for wrapping effects
• Finite-size corrections to the rotating string and the winding state
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• Finite-size effects of beta-deformed AdS_5/CFT_4 at strong coupling
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• Resummation of semiclassical short folded string
• Integrability of Orbifold ABJM Theories
• Integrable systems and AdS/CFT duality
• Integrability of the Gauged Linear Sigma Model for AdS_5xS^5
• Three-Point Functions in ABJM and Bethe Ansatz
• Spectral curve for gamma-deformed AdS/CFT
• Chiral Integrable Boundary States in the SU(4) Alternating Spin Chain
• Semiclassical short strings in AdS_5 x S^5