Twist-two operators and the BFKL regime - nonstandard solutions of the Baxter equation

Abstract

The link between BFKL physics and twist-two operators involves an analytical continuation in the spin of the operators away from the physical even integer values. Typically this is done only after obtaining an analytical result for integer spin through nested harmonic sums. In this paper we propose analyticity conditions for the solution of Baxter equation which would work directly for any value of complex spin and reproduce results from the analytical continuation of harmonic sums. We carry out explicit contructions up to 2-loop level. These nonstandard solutions of the Baxter equation have rather surprising asymptotics. We hope that these analyticity conditions may be used for incorporating them into the exact TBA/FiNLIE/QSC approaches valid at any coupling.

22 pages, 1 figure, Mathematica notebook with numerical checks included in the source submission

References in corpus (8)

• The Pomeron and Gauge/String Duality
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Quantum spectral curve for AdS_5/CFT_4
• Dressing and Wrapping
• Analytic continuation of the Mellin moments of deep inelastic structure functions
• Analytic three-loop Solutions for N=4 SYM Twist Operators
• Scaling dimensions at small spin in N=4 SYM theory
• Approaching the BFKL pomeron via integrable classical solutions

Cited by in corpus (14)

• Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4
• Quantum spectral curve as a tool for a perturbative quantum field theory
• Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM
• QCD Pomeron from AdS/CFT Quantum Spectral Curve
• Wilson loop OPE, analytic continuation and multi-Regge limit
• BFKL Spectrum of N=4 SYM: non-Zero Conformal Spin
• When does the gluon reggeize?
• Regge spectroscopy of higher twist states in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• N=4 SYM Quantum Spectral Curve in BFKL regime
• 2d QCD and Integrability, Part I: 't Hooft model
• Approaching the BFKL pomeron via integrable classical solutions
• Non-linear evolution of unintegrated gluon density at large values of coupling constant
• Exact Results in Supersymmetric Gauge Theories
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory