The Ads/CFT spectrum via Integrability-based algorithms

Abstract

The spectral problem of the AdS/CFT correspondence is believed to be integrable in the planar limit. The Quantum Spectral Curve captures the underlying mathematical structure in a relatively simple Riemann-Hilbert problem. To get physical results from this structure, one needs to solve it explicitly. The main goal of this thesis is the development of efficient algorithms to do this perturbatively for general states in the spectrum. The first step in this procedure is to find a leading solution for each multiplet in the spectrum. This is traditionally done by solving Bethe equations, which is notoriously hard. This thesis outlines a new and more powerful technique, which is also applicable more generally to rational spin chains. It then explains how perturbative corrections can be generated through recursive procedures, and describes a conceptually simple and practically powerful algorithm to do this for general states. This opens the door to a vast range of new spectral data, including 10-loop anomalous dimensions for a variety of multiplets. This data is used to reconstruct the six- and seven-loop contributions to the anomalous dimension of twist-two operators with arbitrary spin. Finally, the thesis discusses the evaluation of Q-operators for non-compact spin chains with the future aim of generating perturbative corrections to these from the Quantum Spectral Curve in mind.