QCD Pomeron from AdS/CFT Quantum Spectral Curve

TL;DR

This paper uses the Quantum Spectral Curve method from integrability to analytically derive the pomeron eigenvalue in planar ${ m N}=4$ SYM, connecting it to BFKL physics and extending the Baxter equation.

Contribution

It analytically continues scaling dimensions using QSC to reproduce the pomeron eigenvalue and generalizes the Baxter equation at next-to-leading order in BFKL.

Findings

Reproduced the pomeron eigenvalue from QSC

Recovered the Baxter equation for Lipatov's spin chain

Extended the Baxter equation to next-to-leading order

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.