The Factorized S-Matrix of CFT/AdS

TL;DR

This paper proposes that the integrability in large-N CFT/AdS systems can be understood through a factorized S-matrix, introducing a new perturbative asymptotic Bethe ansatz to compute it and confirming its consistency with string theory and known anomalous dimensions.

Contribution

The paper introduces a novel perturbative asymptotic Bethe ansatz technique to extract the three-loop S-matrix in the su(1|1) sector of N=4 gauge theory, linking integrability with the factorized S-matrix approach.

Findings

Derived the three-loop S-matrix for the su(1|1) sector.

Confirmed consistency of the S-matrix with semiclassical string results.

Reproduced known three-loop anomalous dimensions of twist-two operators.

Abstract

We argue that the recently discovered integrability in the large-N CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory's dilatation operator nor the string sigma model's quantum Hamiltonian, but instead the respective factorized S-matrix. To illustrate the idea, we focus on the closed fermionic su(1|1) sector of the N=4 gauge theory. We introduce a new technique, the perturbative asymptotic Bethe ansatz, and use it to extract this sector's three-loop S-matrix from Beisert's involved algebraic work on the three-loop su(2|3) sector. We then show that the current knowledge about semiclassical and near-plane-wave quantum strings in the su(2), su(1|1) and sl(2) sectors of AdS_5 x S^5 is fully consistent with the existence of a factorized S-matrix. Analyzing the available information, we find an intriguing relation between the three associated S-matrices. Assuming that the relation also holds in gauge theory, we derive the three-loop S-matrix of the sl(2) sector even though this sector's dilatation operator is not yet known beyond one loop. The resulting Bethe ansatz reproduces the three-loop anomalous dimensions of twist-two operators recently conjectured by Kotikov, Lipatov, Onishchenko and Velizhanin, whose work is based on a highly complex QCD computation of Moch, Vermaseren and Vogt.