On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM

Abstract

Strong evidence indicates that the spectrum of planar anomalous dimensions of N=4 super Yang-Mills theory is given asymptotically by Bethe equations. A curious observation is that the Bethe equations for the psu(1,1|2) subsector lead to very large degeneracies of 2^M multiplets, which apparently do not follow from conventional integrable structures. In this article, we explain such degeneracies by constructing suitable conserved nonlocal generators acting on the spin chain. We propose that they generate a subalgebra of the loop algebra for the su(2) automorphism of psu(1,1|2). Then the degenerate multiplets of size 2^M transform in irreducible tensor products of M two-dimensional evaluation representations of the loop algebra.

35 pages, v2: references added, sign inconsistency resolved in (5.5,5.6), v3: Section 3.4 on Hamiltonian added, minor improvements, to appear in JHEP

References in corpus (29)

• Transcendentality and Crossing
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• On the highest transcendentality in N=4 SUSY
• On the Singularities of the Magnon S-matrix
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• On the Hopf algebra structure of the AdS/CFT S-matrix
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Four-Loop Cusp Anomalous Dimension From Obstructions
• On the Strong Coupling Scaling Dimension of High Spin Operators
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• The WZNW model on PSU(1,1|2)
• Strong coupling limit of Bethe Ansatz equations
• The magnon kinematics of the AdS/CFT correspondence
• 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
• Classical r-matrix of the su(2|2) SYM spin-chain
• The scaling function at strong coupling from the quantum string Bethe equations
• A Yangian Double for the AdS/CFT Classical r-matrix
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Quantum deformed magnon kinematics
• Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM
• Tensor products of psl(2|2) representations
• Analytic Bethe Ansatz and Baxter equations for long-range psl(2|2) spin chain

Cited by in corpus (27)

• Integrability and the AdS(3)/CFT(2) correspondence
• The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector
• Integrability, spin-chains and the AdS3/CFT2 correspondence
• Giant magnons in the D1-D5 system
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
• Tailoring Non-Compact Spin Chains
• Yangians, S-matrices and AdS/CFT
• Weakly Renormalized Near 1/16 SUSY Fermi Liquid Operators in N = 4 SYM
• Aspects of Non-Relativistic Quantum Field Theories
• Giant magnon bound states from strongly coupled N=4 SYM
• Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
• The su(2|3) Undynamic Spin Chain
• Structure of the string R-matrix
• The Panorama of Spin Matrix Theory
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin
• Degenerate Rotating Black Holes, Chiral CFTs and Fermi Surfaces I - Analytic Results for Quasinormal Modes
• Dynamic Lattice Supersymmetry in gl(n|m) Spin Chains
• Chiral 2D "Strange Metals" from N = 4 SYM
• Yangians in Deformed Super Yang-Mills Theories
• Symmetry structure of the interactions in near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory