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      Dressing phases of AdS3/CFT2

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          Abstract

          We determine the all-loop dressing phases of the AdS3/CFT2 integrable system related to type IIB string theory on AdS3 x S3 x T4 by solving the recently found crossing relations and studying their singularity structure. The two resulting phases present a novel structure with respect to the ones appearing in AdS5/CFT4 and AdS4/CFT3. In the strongly-coupled regime, their leading order reduces to the universal Arutyunov-Frolov-Staudacher phase as expected. We also compute their sub-leading order and compare it with recent one-loop perturbative results, and comment on their weak-coupling expansion.

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          Transcendentality and Crossing

          We discuss possible phase factors for the S-matrix of planar N=4 gauge theory, leading to modifications at four-loop order as compared to an earlier proposal. While these result in a four-loop breakdown of perturbative BMN-scaling, Kotikov-Lipatov transcendentality in the universal scaling function for large-spin twist operators may be preserved. One particularly natural choice, unique up to one constant, modifies the overall contribution of all terms containing odd zeta functions in the earlier proposed scaling function based on a trivial phase. Excitingly, we present evidence that this choice is non-perturbatively related to a recently conjectured crossing-symmetric phase factor for perturbative string theory on AdS_5xS^5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve the long-standing AdS/CFT discrepancies between gauge and string theory.
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            Magnon Bound States and the AdS/CFT Correspondence

            Nick Dorey (2006)
            We study the spectrum of asymptotic states in the spin-chain description of planar N=4 SUSY Yang-Mills. In addition to elementary magnons, the asymptotic spectrum includes an infinite tower of multi-magnon bound states with exact dispersion relation, Delta-J_{1} = sqrt{Q^{2}+(lambda/pi^2)sin^2(p/2)}, where the positive integer Q is the number of constituent magnons. These states account precisely for the known poles in the exact S-matrix. Like the elementary magnon, they transform in small representations of supersymmetry and are present for all values of the 't Hooft coupling. At strong coupling we identify the dual states in semiclassical string theory.
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              On the Singularities of the Magnon S-matrix

              We investigate the analytic structure of the magnon S-matrix in the spin-chain description of planar \({\cal N}=4\) SUSY Yang-Mills/\(AdS_{5}\times S^{5}\) strings. Semiclassical analysis suggests that the exact S-matrix must have a large family of poles near the real axis in momentum space. In this article we show that these are double poles corresponding to the exchange of pairs of BPS magnons. Their locations in the complex plane are uniquely fixed by the known dispersion relation for the BPS particles. The locations precisely agree with the recent conjecture for the \(S\) matrix by Beisert, Hernandez, Lopez, Eden and Staudacher (hep-th/0609044 and hep-th/0610251). These poles do not signal the presence of new bound states. In fact, a certain non-BPS localized classical solution, which was thought to give rise to new bound states, can actually decay into a pair of BPS magnons.
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                Author and article information

                Journal
                11 June 2013
                2013-06-27
                Article
                10.1103/PhysRevD.88.066004
                1306.2512
                8b6ef220-20a9-4b3b-8666-867a96767b05

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                DMUS-MP-13/14; ITP-UU-13/14; SPIN-13/10
                29 pages, 4 figures; v2: note added, minor changes
                hep-th

                High energy & Particle physics
                High energy & Particle physics

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