Quantum spectral curve for AdS_5/CFT_4

TL;DR

This paper introduces a new formalism using a non-linear matrix Riemann-Hilbert problem with Q-functions to solve the spectral problem in planar N=4 SYM, offering an alternative to traditional TBA methods.

Contribution

It proposes a concise, alternative approach to the spectral problem in N=4 SYM using Riemann-Hilbert problems and Q-functions, simplifying previous methods.

Findings

Successfully applied to local operators at weak coupling.

Demonstrated effectiveness for cusped Wilson lines near BPS limit.

Provides a more streamlined formalism compared to TBA approaches.

Abstract

We present a new formalism, alternative to the old TBA-like approach, for solution of the spectral problem of planar N = 4 SYM. It takes a concise form of a non-linear matrix Riemann-Hilbert problem in terms of a few Q-functions. We demonstrate the formalism for two types of observables - local operators at weak coupling and cusped Wilson lines in a near BPS limit.