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QCD Pomeron from AdS/CFT Quantum Spectral Curve

Mikhail Alfimov, Nikolay Gromov, Vladimir Kazakov

Abstract

Using the methods of the recently proposed Quantum Spectral Curve (QSC) originating from integrability of ${\cal N}=4$ Super--Yang-Mills theory we analytically continue the scaling dimensions of twist-2 operators and reproduce the so-called pomeron eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. Furthermore, we recovered the Faddeev-Korchemsky Baxter equation for Lipatov's spin chain and also found its generalization for the next-to-leading order in the BFKL scaling. Our results provide a non-trivial test of QSC describing the exact spectrum in planar ${\cal N}=4$ SYM at infinitely many loops for a highly nontrivial non-BPS quantity and also opens a way for a systematic expansion in the BFKL regime.

QCD Pomeron from AdS/CFT Quantum Spectral Curve

Abstract

Using the methods of the recently proposed Quantum Spectral Curve (QSC) originating from integrability of Super--Yang-Mills theory we analytically continue the scaling dimensions of twist-2 operators and reproduce the so-called pomeron eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. Furthermore, we recovered the Faddeev-Korchemsky Baxter equation for Lipatov's spin chain and also found its generalization for the next-to-leading order in the BFKL scaling. Our results provide a non-trivial test of QSC describing the exact spectrum in planar SYM at infinitely many loops for a highly nontrivial non-BPS quantity and also opens a way for a systematic expansion in the BFKL regime.

Paper Structure

This paper contains 21 sections, 79 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Motivation from Weak Coupling
  3. Quantum Spectral Curve -- Generalities
  4. Algebraic properties:
  5. From ${\bf P}_a$ to ${\bf Q}_i$.
  6. Analytic properties:
  7. ${\bf P}\mu$-system.
  8. ${\bf Q}\omega$-system.
  9. Quantum Spectral Curve for Twist-2 Operators
  10. Prescription for analytic continuation in $S$.
  11. Leading Order solution for ${\bf P}\mu$-system
  12. Next-to-Leading-Order solution
  13. Passing to ${\bf Q}\omega$-system
  14. NLO Baxter equation.
  15. Going to the next sheet
  16. ...and 6 more sections

Figures (2)

  • Figure 1: Cut structure of ${\bf P}$ and $\mu$, ${\bf Q}$ and $\omega$ and their analytic continuations $\tilde{{\bf P}}$ and $\tilde{\mu}$, $\tilde{{\bf Q}}$ and $\tilde{\omega}$Gromov:2013pgaGromov:2014caa
  • Figure 2: Regge trajectories $S(\Delta)$ corresponding to the twist 2 operator ${\rm tr}\,Z (D_+)^S Z$ and different values of $g$.