The Factorized S-Matrix of CFT/AdS

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.

38 pages, LaTeX, JHEP3.cls

References in corpus (11)

• Bethe Ansatz for Quantum Strings
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• Integrability in QCD and beyond
• Classical/quantum integrability in non-compact sector of AdS/CFT
• On one-loop correction to energy of spinning strings in S^5
• A three-loop test of the dilatation operator in N=4 SYM
• N-Impurity Superstring Spectra Near the pp-Wave Limit
• Spin chain sigma models with fermions
• Lattice Super Yang-Mills: A Virial Approach to Operator Dimensions
• N=4 Super-Yang-Mills Theory, QCD and Collider Physics

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