Integrable structures and duality in high-energy QCD

Abstract

We study the properties of color-singlet Reggeon compound states in multicolor high-energy QCD in four dimensions. Their spectrum is governed by completely integrable (1+1)-dimensional effective QCD Hamiltonian whose diagonalization within the Bethe Ansatz leads to the Baxter equation for the Heisenberg spin magnet. We show that nonlinear WKB solution of the Baxter equation gives rise to the same integrable structures as appeared in the Seiberg-Witten solution for $N=2$ SUSY QCD and in the finite-gap solutions of the soliton equations. We explain the origin of hyperelliptic Riemann surfaces out of QCD in the Regge limit and discuss the meaning of the Whitham dynamics on the moduli space of quantum numbers of the Reggeon compound states, QCD Pomerons and Odderons.

30 pages, LaTeX style, 3 figures embedded with epsf.sty

References in corpus (19)

• Supersymmetric Yang-Mills Systems And Integrable Systems
• Separation of Variables. New Trends.
• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• Integrability and Seiberg-Witten Exact Solution
• The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
• Integrable systems and supersymmetric gauge theory
• On the Quantum Moduli Space of Vacua of $N=2$ Supersymmetric $SU(N_c)$ Gauge Theories
• Integrability and Seiberg-Witten Theory: Curves and Periods
• Prepotentials of $N=2$ Supersymmetric Gauge Theories and Soliton Equations
• On the Monodromies of N=2 Supersymmetric Yang-Mills Theory with Gauge Group SO(2n)
• Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory
• The Moduli Space and Monodromies of N=2 Supersymmetric \(SO(2r+1) \) Yang-Mills Theory
• Integrable Structures in Supersymmetric Gauge and String Theory
• N=2 Supersymmetric QCD and Integrable Spin Chains: Rational Case N_f < 2N_c
• Bethe Ansatz for QCD Pomeron,
• Quasiclassical QCD Pomeron
• Isomonodromic deformations and supersymmetric gauge theories
• Baxter Equation for the QCD Odderon
• Modular Invariance and the Odderon

Cited by in corpus (29)

• Classical/quantum integrability in AdS/CFT
• Baryon Distribution Amplitudes in QCD
• Logarithmic scaling in gauge/string correspondence
• Anomalous dimensions of high-spin operators beyond the leading order
• Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains
• Integrability of Conformal Fishnet Theory
• Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
• Noncompact Heisenberg spin magnets from high-energy QCD: II. Quantization conditions and energy spectrum
• The Odderon in Quantum Chromodynamics
• Reggeon Field Theory for Large Pomeron Loops
• Twist 3 of the sl(2) sector of N=4 SYM and reciprocity respecting evolution
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• The Odderon in High Energy Elastic pp Scattering
• Solitons in high-energy QCD
• From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy
• QCD Reggeon Calculus From KLWMIJ/JIMWLK Evolution: Vertices, Reggeization and All
• Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM
• Reciprocity of gauge operators in N=4 SYM
• High Energy QCD: Stringy Picture from Hidden Integrability
• Noncompact Heisenberg spin magnets from high-energy QCD: III. Quasiclassical approach
• Gauge Theories as String Theories: the First Results
• Quasiclassical Geometry and Integrability of AdS/CFT Correspondence
• 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
• Inside looking out: probing JIMWLK with BFKL calculations
• Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains
• Eikonal but not: a complementary view of high energy evolution
• Large Nc gauge theory with quarks in high representations
• Baryon wave functions in QCD and integrable models