The full Quantum Spectral Curve for $AdS_4/CFT_3$

TL;DR

This paper develops the full Quantum Spectral Curve for the $AdS_4/CFT_3$ duality, enabling finite-coupling spectral analysis of the N=6 superconformal Chern-Simons theory using integrability techniques.

Contribution

It introduces the complete Quantum Spectral Curve for $AdS_4/CFT_3$ and embeds it into a novel Q-system reflecting the theory's symmetry, advancing integrability methods.

Findings

Quantum Spectral Curve for $AdS_4/CFT_3$ is fully formulated.

Embedded into a new Q-system with $OSp(4|6)$ symmetry.

Derived exact Bethe Ansatz equations for the theory.

Abstract

The spectrum of planar N=6 superconformal Chern-Simons theory, dual to type IIA superstring theory on $AdS_4 \times CP^3$, is accessible at finite coupling using integrability. Starting from the results of [arXiv:1403.1859], we study in depth the basic integrability structure underlying the spectral problem, the Quantum Spectral Curve. The new results presented in this paper open the way to the quantitative study of the spectrum for arbitrary operators at finite coupling. Besides, we show that the Quantum Spectral Curve is embedded into a novel kind of Q-system, which reflects the OSp(4|6) symmetry of the theory and leads to exact Bethe Ansatz equations. The discovery of this algebraic structure, more intricate than the one appearing in the $AdS_5/CFT_4$ case, could be a first step towards the extension of the method to $AdS_3/CFT_2$.