Integrability for the Full Spectrum of Planar AdS/CFT

TL;DR

This paper introduces a comprehensive set of functional equations, based on integrability, that precisely determine the anomalous dimensions of all local operators in planar N=4 SYM theory, confirming previous results and extending to AdS_4/CFT_3.

Contribution

It formulates a Y-system that captures the full spectrum of planar N=4 SYM, integrating asymptotic Bethe ansatz, dressing factors, and wrapping corrections, and applies similar methods to AdS_4/CFT_3 duality.

Findings

Y-system accurately reproduces known anomalous dimensions

Incorporates dressing factors and wrapping corrections

Validates AdS_4/CFT_3 duality predictions

Abstract

We present a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar N=4 SYM theory. It takes the form of a Y-system based on the integrability of the dual superstring sigma-model on the AdS_5xS^5 background. This Y-system passes some very important tests: it incorporates the full asymptotic Bethe ansatz at large length of operator L, including the dressing factor, and it confirms all recently found wrapping corrections. The recently proposed AdS_4/CFT_3 duality is also treated in a similar fashion.