Quantum spectral curve for AdS_5/CFT_4

TL;DR

The paper introduces the Pμ system, a concise non-linear Riemann-Hilbert formulation for the AdS5/CFT4 spectral problem that replaces the traditional TBA. It expresses the spectrum through a small set of Q-functions via precise analytic continuation rules, enabling reconstruction of Y- and T-functions and a complete spectral curve. In the weak-coupling regime, it reproduces a Baxter-like equation and Bethe roots, yielding the one-loop dimension, while for cusped Wilson lines it recovers the known cusp anomalous dimension, demonstrating broad applicability. This framework offers new avenues for tackling strong coupling, BFKL regimes, and connects to Q-system structures and physical T-hooks, suggesting a unified all-loop picture.

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.

Figures (2)

• Figure 1: T-hook: lattice for the AdS/CFT T-system
• Figure 2: Cut structure of ${\bf P}$ and $\mu$