Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings

Abstract

We generalize various existing higher-loop Bethe ansaetze for simple sectors of the integrable long-range dynamic spin chain describing planar N=4 Super Yang-Mills Theory to the full psu(2,2|4) symmetry and, asymptotically, to arbitrary loop order. We perform a large number of tests of our conjectured equations, such as internal consistency, comparison to direct three-loop diagonalization and expected thermodynamic behavior. In the special case of the su(1|2) subsector, corresponding to a long-range t-J model, we are able to derive, up to three loops, the S-matrix and the associated nested Bethe ansatz from the gauge theory dilatation operator. We conjecture novel all-order S-matrices for the su(1|2) and su(1,1|2) subsectors, and show that they satisfy the Yang-Baxter equation. Throughout the paper, we muse about the idea that quantum string theory on AdS_5xS^5 is also described by a psu(2,2|4) spin chain. We propose asymptotic all-order Bethe equations for this putative "string chain", which differ in a systematic fashion from the gauge theory equations.

67 pages, In Honor of Hans Bethe, v2: references added, typos fixed, sign conventions improved, v3: published version

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• Three-point functions at strong coupling in the BMN limit
• Strong Wilson polygons from the lodge of free and bound mesons
• Is there a tower of charges to be discovered?
• Analytic Bethe Ansatz and Baxter equations for long-range psl(2|2) spin chain
• N=1 SQCD and the Transverse Field Ising Model
• Asymptotic Bethe equations for open boundaries in planar AdS/CFT
• Y-system for $\gamma$-deformed ABJM Theory
• Strong coupling from the Hubbard model
• OPE in planar QCD from integrability
• Integrability and the AdS/CFT correspondence
• Yangian Symmetry in N=4 super Yang-Mills
• Integrability treatment of AdS/CFT orbifolds
• Giant Holes
• Level density distribution for one-dimensional vertex models related to Haldane-Shastry like spin chains
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• From Quantum Affine Symmetry to Boundary Askey-Wilson Algebra and Reflection Equation
• Reciprocity and integrability in the sl(2) sector of N=4 SYM
• The virtual scaling function of twist operators in the N=6 Chern-Simons theory
• Unified approach to the SU(2) Principal Chiral Field model at Finite Volume
• Approaching the BFKL pomeron via integrable classical solutions
• Close to the Giant Magnons
• Integrability of Orbifold ABJM Theories
• Superconformal invariance from N=2 supersymmetry Ward identities
• A novel quasi-exactly solvable spin chain with nearest-neighbors interactions
• QCD-like properties for anomalous dimensions in N=4 SYM
• Jordan blocks and the Bethe ansatz II: The eclectic spin chain beyond $K=1$
• Four-loop anomalous dimensions in Leigh-Strassler deformations
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Integrable systems and AdS/CFT duality
• On analytical perturbative solution of ABJM quantum spectral curve
• Bethe Ansatz for Quantum-Deformed Strings
• The Ising model and planar N=4 Yang-Mills
• Exact result in N=4 SYM theory: Generalised double-logarithmic equation
• Aspects of Integrability in N =4 SYM
• Wrapping corrections for non-diagonal boundaries in AdS/CFT
• Giant Spinons
• The full spectrum of AdS${}_5$/CFT${}_4$ II: Weak coupling expansion via the quantum spectral curve
• Microscopic formulation of the S-matrix in AdS/CFT
• Highest states in light-cone $Ad{S}_5\times S^5$ superstring
• Excited States of Open Strings From $\mathcal{N}=4$ SYM
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Wrapping effects in supersymmetric gauge theories
• Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
• Dilatation operator in 3d
• Nonplanar Four-Loop Anomalous Dimensions of Twist-Two Operators in N=4 Super Yang-Mills Theory: Higher Moment, General Result, and Cusp Anomalous Dimension
• Integrability of the Gauged Linear Sigma Model for AdS_5xS^5
• BMN operators with a scalar fermion pair and operator mixing in N=4 Super Yang-Mills Theory
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• The complete unitary dual of non-compact Lie superalgebra su(p,q|m) via the generalised oscillator formalism, and non-compact Young diagrams
• PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets
• Exact results for the low energy AdS(4)XCP(3) string theory
• Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
• Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops
• Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Chaotic string motion in a near pp-wave limit
• Quantum dispersion relations for the $Ad{S}_4\times C{P}^3$ GKP string
• Analytic Bethe Ansatz Solutions for Highest States in the su(1|1) and su(2) Sectors
• Exact Results in Supersymmetric Gauge Theories
• On the one-loop curvature function in the $sl(2)$ sector of $\mathcal{N}=4$ SYM
• Spectral curve for gamma-deformed AdS/CFT
• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Thermodynamical limit of general gl(N) spin chains II: Excited states and energies
• Yangian Symmetry, S-Matrices and Bethe Ansatz for the AdS5 x S5 Superstring
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices
• Bound State Scattering Simplified
• Mass-Gaps and Spin Chains for (Super) Membranes
• The SU(2) Long Range Bethe Ansatz and Continuous Integrable Systems
• Finite-size Effect for Dyonic Giant Magnons in $C{P}_{\beta }^3$
• A semiclassical analysis of the fluctuation eigenvalues and the one-loop energy of the folded spinning superstring in AdS_5 x S^5
• Finite Size Effect from Classical Strings in deformed AdS${}_3\times$ S${}^3$
• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5
• Pomeron in the N=4 SYM at strong couplings
• Spiky Strings with Two Spins in AdS5
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM
• Fermionic contribution to the anomalous dimension of twist-2 operators in N=4 SYM theory, critical indices and integrability
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory
• Pomeron in the N=4 SYM
• Comments on the slope function