The factorized S-matrix of CFT/AdS

By M. Staudacher. 2004

567 citations recorded by the source corpus.

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 (1|1) sector of the = 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 (2|3) sector. We then show that the current knowledge about semiclassical and near-plane-wave quantum strings in the (2), (1|1) and (2) sectors of AdS5 × S5 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 (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.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/431ea52127b0f131865d7bc8274a13cd50a1f03b

How researchers see this paper

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In Geometry and Topology

1. S. Frolov
2. G. Arutyunov
3. N. Beisert
4. A. Tseytlin
5. Romuald A. Janik
6. K. Zarembo
7. R. Roiban
8. Tomasz Lukowski

In Mathematical Physics

1. S. Frolov
2. K. Zarembo
3. A. Tseytlin
4. R. Roiban
5. G. Arutyunov
6. N. Beisert
7. Romuald A. Janik
8. M. Staudacher

In Nuclear and High Energy Physics

1. S. Frolov
2. N. Beisert
3. G. Arutyunov
4. A. Tseytlin
5. M. Staudacher
6. Romuald A. Janik
7. R. Roiban
8. K. Zarembo

Citations in the corpus

• Planar N = 4 gauge theory and the Hubbard model (2005, background): “Actually, the asymptotic BDS ansatz may even be modified to include non-compact sectors such as sl(2) [33], and lifted to the complete theory [34], with symmetry psu(2, 2|4).”
• A Crossing-Symmetric Phase for AdS5 x S5 Strings (2006, unknown): “The asymptotic Bethe ansätze for gauge and string theory are very similar, and the asymptotic S-matrices on each side of the correspondence differ simply by a scalar factor [10,5].”
• Magnon bound states and the AdS/CFT correspondence (2006, background): “These states are in short representations of the supersymmetry which essentially determines their dispersion relation as(1) [10, 11, 12, 13] (see also [14]), ∆− J1 = √”
• Transcendentality and crossing (2006, methodology): “Firstly, it turns out that an asymptotic ‘world-sheet’ S-matrix of this theory may be defined, in the planar limit, in an internal space [1].”
• Wrapping interactions at strong coupling: The giant magnon (2007, unknown): “22 08 ∗e-mail: ufrjanik@if.uj.edu.pl †e-mail: tomaszlukowski@gmail.com”
• Gauge-string duality for (non)supersymmetric deformations of N=4 super-Yang–Mills theory (2005, background): “est su(2)γ case in [2]). One may also hope that the analysis of the string Bethe equations will shed light on the structure of the dressing factor that appears in the Bethe ansatz for quantum strings [48, 49, 50] (in the deformed case the dressing factor may depend on γiand that may lead to an addit”
• The analytic Bethe ansatz for a chain with centrally extended symmetry (2006, methodology): “The S-matrix [16, 9, 18] describes the asymptotic wavefunctions of multi-particle states on a vacuum of infinite length.”
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory (2009, background): “On the gauge theory side the problem of finding the all-loop scaling dimensions can be mapped to the eigenvalue problem of a long-range integrable spin chain model, which in turn is governed by a nested set of Bethe equations [8] (see [9] for reviews), for recent progress see [10].”
• Quantum corrections to the string Bethe ansatz (2006, background): “We are assuming that the modified dressing phase (7) is common for all sectors of the correspondence, as it was the case in [12, 13].”