Integrability and WKB solution of twist-three evolution equations

Abstract

We identify an integrable one-dimensional inhomogeneous three-site open spin chain which arises in the problem of diagonalization of twist-three quark-gluon evolution equations in QCD in the chiral-odd sector. Making use of the existence of a non-trivial `hidden' integral of motion the problem of diagonalization of the evolution kernels is reduced to the study of a second order finite-difference equation which is solved in WKB approximation for large conformal spins of the three-particle system. The energies (alias anomalous dimensions) of eigenstates with different scale dependence are found in limiting cases and compared with numerical calculations.

26 pages, LaTeX, 4 figures; typos fixed

References in corpus (10)

• Integrability of three-particle evolution equations in QCD
• Broken conformal invariance and spectrum of anomalous dimensions in QCD
• Fine structure of spectrum of twist-three operators in QCD
• Polarized Structure Functions in QCD
• Scale dependence of the chiral-odd twist-3 distributions $h_L(x)$ and $e(x)$
• Duality symmetry of Reggeon interactions in multicolour QCD
• Next-to-leading order evolution of twist-two conformal operators: The abelian case
• A_{LT} in the polarized Drell-Yan process at RHIC and HERA energies
• Evolution of twist-3 fragmentation functions in multicolour QCD and the Gribov-Lipatov reciprocity
• High-energy scattering in gauge theories and integrable spin chains

Cited by in corpus (79)

• Unraveling hadron structure with generalized parton distributions
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• The su(2|3) Dynamic Spin Chain
• The Uses of Conformal Symmetry in QCD
• Spin chains and string theory
• SU(N) gauge theories at large N
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
• Matching Higher Conserved Charges for Strings and Spins
• Gauge/string duality for QCD conformal operators
• Logarithmic scaling in gauge/string correspondence
• Anomalous dimensions of high-spin operators beyond the leading order
• Spiky strings and single trace operators in gauge theories
• Integrability in QCD and beyond
• Twist-three effects in two-photon processes
• Evolution of twist-3 multi-parton correlation functions relevant to single transverse-spin asymmetry
• Next-to-leading Order Calculation of the Single Transverse Spin Asymmetry in the Drell-Yan Process
• Spiky strings and giant magnons on S5
• Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
• N=4 SUSY Yang--Mills: three loops made simple(r)
• Dilatation operator in (super-)Yang-Mills theories on the light-cone
• QCD Evolution of the Transverse Momentum Dependent Correlations
• Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
• Superconformal operators in N=4 super-Yang-Mills theory
• A Complete Basis of Helicity Operators for Subleading Factorization
• Integrability of scattering amplitudes in N=4 SUSY
• On spin chains and field theories
• Separation of variables for the quantum SL(2,R) spin chain
• Baryon Operators of Higher Twist in QCD and Nucleon Distribution Amplitudes
• Quantum integrability in (super) Yang-Mills theory on the light-cone
• Integrable Open Spin Chains in Defect Conformal Field Theory
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Pulsating Strings on AdS_5 x S^5
• Non-local charges on AdS_5 x S^5 and PP-waves
• Subleading Power Factorization with Radiative Functions
• Noncompact Heisenberg spin magnets from high-energy QCD: II. Quantization conditions and energy spectrum
• Quantum integrability and functional equations
• Higher Conserved Charges and Integrability for Spinning Strings in AdS_5 x S^5
• On Yangian Symmetry in Planar N=4 SYM
• Evolution equation for the structure function g_2(x,Q^2)
• Open Spinning Strings
• Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality
• Duality between Wilson loops and gluon amplitudes
• Integrability of two-loop dilatation operator in gauge theories
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• Towards Baxter equation in supersymmetric Yang-Mills theories
• Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation
• The Circular, Elliptic Three Spin String from the SU(3) Spin Chain
• Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM
• Spin Models and Superconformal Yang-Mills Theory
• Spiky Strings and Spin Chains
• The Singlet g_2 Structure Function in the Next-to-Leading Order
• Crosscap States in Integrable Field Theories and Spin Chains
• Evolution Equation for Generalized Parton Distributions
• High Energy QCD: Stringy Picture from Hidden Integrability
• Multi-spin string solutions in AdS Black Hole and confining backgrounds
• OPE for null Wilson loops and open spin chains
• Noncompact SL(2,R) spin chain
• Integrable spin chains and scattering amplitudes
• Fusion hierarchies for N = 4 superYang-Mills theory
• Renormalization of twist-four operators in light-cone gauge
• Multi-reggeon compound states and resummed anomalous dimensions in QCD
• Integrability in heavy quark effective theory
• Bethe ansatz equations for open spin chains from giant gravitons
• Solving the leading order evolution equation for GPDs
• Gauge Theories as String Theories: the First Results
• Parton interaction in super Yang Mills theory
• TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• Separation of Variables for a flux tube with an end
• Universal R operator with Jordanian deformation of conformal symmetry
• Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains
• Renormalization group flow of reduced string actions
• QCD Beyond Leading Power
• Baryon wave functions in QCD and integrable models
• Transverse momentum dependent quark distributions and polarized Drell-Yan processes