Complete Spectrum of Long Operators in N=4 SYM at One Loop

Abstract

We construct the complete spectral curve for an arbitrary local operator, including fermions and covariant derivatives, of one-loop N=4 gauge theory in the thermodynamic limit. This curve perfectly reproduces the Frolov-Tseytlin limit of the full spectral curve of classical strings on AdS_5xS^5 derived in hep-th/0502226. To complete the comparison we introduce stacks, novel bound states of roots of different flavors which arise in the thermodynamic limit of the corresponding Bethe ansatz equations. We furthermore show the equivalence of various types of Bethe equations for the underlying su(2,2|4) superalgebra, in particular of the type "Beauty" and "Beast".

Dedicated to the memory of Hans Bethe, 50 pages, v2: references added, minor corrections, v3: reference, typo, to appear in JHEP

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• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Integrability and the AdS(3)/CFT(2) correspondence
• Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• The all loop AdS4/CFT3 Bethe ansatz
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• Spinning strings and integrable spin chains in the AdS/CFT correspondence
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• On Quantum Corrections to Spinning Strings and Bethe Equations
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• The AdS4/CFT3 algebraic curve
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• Exciting the GKP string at any coupling
• Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
• Baxter's Q-operators for supersymmetric spin chains
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Complete 1-loop test of AdS/CFT
• A Universality Test of the Quantum String Bethe Ansatz
• Stringy sums and corrections to the quantum string Bethe ansatz
• Tailoring Three-Point Functions and Integrability III. Classical Tunneling
• Bethe Ansatz for a Quantum Supercoset Sigma Model
• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• Worldsheet spectrum in AdS(4)/CFT(3) correspondence
• Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• Lectures on the Bethe Ansatz
• Y-system and Quasi-Classical Strings
• Finite-Size Effects for Dyonic Giant Magnons
• Comment on the Scaling Function in AdS4 x CP3
• Wronskian Solution for AdS/CFT Y-system
• Quantum Wrapped Giant Magnon
• Constructing the AdS/CFT dressing factor
• Strings as Multi-Particle States of Quantum Sigma-Models
• Classical tau-function for quantum spin chains
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• The full Quantum Spectral Curve for $Ad{S}_4/CF{T}_3$
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• $Ad{S}_3/CF{T}_2$, finite-gap equations and massless modes
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• Twisted Bethe equations from a twisted S-matrix
• Double Scaling and Finite Size Corrections in sl(2) Spin Chain
• 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
• Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability
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• Discrete Hirota dynamics for AdS/CFT
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• Wound and Rotating Strings in AdS_5 x S^5
• Leading transcedental contribution to the four-loop universal anomalous dimension in N=4 SYM
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• Bethe Ansatz Equations for General Orbifolds of N=4 SYM
• From Polygon Wilson Loops to Spin Chains and Back
• Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• Fusion hierarchies for N = 4 superYang-Mills theory
• Y-system for Y=0 brane in planar AdS/CFT
• Sigma model from SU(1,1|2) spin chain
• The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: first moments in N=4 SYM and non-singlet QCD
• A large spin limit of strings on AdS_5 x S^5 in a non-compact sector
• AdS/CFT v.s. String Loops
• Non-planar anomalous dimension of twist-2 operators: higher moments at four loops
• Nesting and Dressing
• Two-Loop Spectroscopy of Short ABJM Operators
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• On the origin of the dressing phase in N=4 Super Yang-Mills
• The spectrum of quantum-group-invariant transfer matrices
• Strong coupling anomalous dimensions of $\mathcal{N}=4$ super Yang-Mills
• Testing the nested light-cone Bethe equations of the AdS_5 x S^5 superstring
• Analytic Bethe Ansatz and Baxter equations for long-range psl(2|2) spin chain
• Revisiting the Y=0 open spin chain at one loop
• Nested algebraic Bethe ansatz for open GL(N) spin chains with projected K-matrices
• Microscopic formulation of the S-matrix in AdS/CFT
• Wrapping effects in supersymmetric gauge theories
• Excited States of Open Strings From $\mathcal{N}=4$ SYM
• Giant Spinons
• Nonplanar Four-Loop Anomalous Dimensions of Twist-Two Operators in N=4 Super Yang-Mills Theory: Higher Moment, General Result, and Cusp Anomalous Dimension
• Asymptotic Bethe ansatz of ABJM open spin chain from giant graviton
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• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Flag Integrable Models and Generalized Graded Algebras
• Novel aspects of integrability for NLSMs in symmetric spaces