Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM

Abstract

Recently, several multi-loop conjectures have been proposed for the spin dependence of anomalous dimensions of twist-2 and 3 operators in the sl(2) sector of N=4 SYM. Currently, these conjectures are not proven, although several consistency checks have been performed on their large spin expansion. In this paper, we show how these expansions can be efficiently computed without resorting to any conjecture. To this aim we present in full details a method to expand at large spin the solution of the long-range Baxter equation. We treat the twist-2 and 3 cases at two loops and the twist-3 case at three loops. Several subtleties arise whose resolution leads to a simple algorithm computing the expansion.

arXiv comment26 pages

References in corpus (40)

• Gauge Theory Correlators from Non-Critical String Theory
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• The N=4 SYM Integrable Super Spin Chain
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Bethe Ansatz for Quantum Strings
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• High energy QCD as a completely integrable model
• The Factorized S-Matrix of CFT/AdS
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Quantum corrections to the string Bethe ansatz
• Integrability of three-particle evolution equations in QCD
• On String S-matrix, Bound States and TBA
• Dressing and Wrapping
• Logarithmic scaling in gauge/string correspondence
• Anomalous dimensions of high-spin operators beyond the leading order
• Integrability in QCD and beyond
• Wrapping interactions at strong coupling -- the giant magnon
• On the Hopf algebra structure of the AdS/CFT S-matrix
• Integrability and Transcendentality
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains
• Baxter's Q-operator for the homogeneous XXX spin chain
• Bethe Ansatz for QCD Pomeron,
• Quasiclassical QCD Pomeron
• N=4 SUSY Yang--Mills: three loops made simple(r)
• Dilatation operator in (super-)Yang-Mills theories on the light-cone
• Separation of variables for the quantum SL(2,R) spin chain
• N=4 SYM to Two Loops: Compact Expressions for the Non-Compact Symmetry Algebra of the su(1,1|2) Sector
• Long-range SL(2) Baxter equation in N=4 super-Yang-Mills theory
• Integrability of two-loop dilatation operator in gauge theories
• Twist 3 of the sl(2) sector of N=4 SYM and reciprocity respecting evolution
• 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
• A two-loop test for the factorised S-matrix of planar N=4
• Integrability in Yang-Mills theory on the light cone beyond leading order
• Baxter equation for long-range SL(2|1) magnet
• Universality of three gaugino anomalous dimensions in N=4 SYM

Cited by in corpus (8)

• Twist-three at five loops, Bethe Ansatz and wrapping
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• Luescher formula for GKP string
• On wrapping corrections to GKP-like operators
• Integrability in heavy quark effective theory
• QCD-like properties for anomalous dimensions in N=4 SYM
• Large spin expansion of the wrapping correction to Freyhult-Rej-Zieme twist operators