Integrability and WKB solution of twist-three evolution equations

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88 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)259-284
Number of pages26
JournalNuclear Physics B
Issue number1-2
StatePublished - Oct 4 1999
Externally publishedYes


  • Evolution
  • Integrability
  • Open spin chain
  • Spectrum of eigenvalues
  • Three-particle problem
  • Twist-three operators

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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