Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4

TL;DR

This paper introduces a fast, precise numerical algorithm based on the Quantum Spectral Curve for computing the spectrum of anomalous dimensions in planar N=4 Super-Yang-Mills theory at finite coupling, applicable to generic states.

Contribution

The authors develop a novel numerical method using the Quantum Spectral Curve formalism that surpasses previous approaches in speed and applicability for generic operators in AdS5/CFT4.

Findings

Accurately computed dimensions of twist operators for any spin S.

Determined the BFKL pomeron intercept with up to 20 significant figures.

Explored the complex branch cut structure of the spectral problem.

Abstract

We developed an efficient numerical algorithm for computing the spectrum of anomalous dimensions of the planar ${\cal N}=4$ Super-Yang--Mills at finite coupling. The method is based on the Quantum Spectral Curve formalism. In contrast to Thermodynamic Bethe Ansatz, worked out only for some very special operators, this method is applicable for generic states/operators and is much faster and precise due to its Q-quadratic convergence rate. To demonstrate the method we evaluate the dimensions $\Delta$ of twist operators in $sl(2)$ sector directly for any value of the spin $S$ including non-integer values. In particular, we compute the BFKL pomeron intercept in a wide range of the 't Hooft coupling constant with up to $20$ significant figures precision, confirming two previously known from the perturbation theory orders and giving prediction for several new coefficients. Furthermore, we explore numerically a rich branch cut structure for complexified spin $S$.