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130
Generalized scaling function from lightcone gauge
 AdS5 × S5 superstring,” JHEP 1006, 060 (2010) [arXiv:1002.0018
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qdeformed supersymmetry and dynamic magnon representations,” arXiv:0704.2069 [hepth
"... It was recently noted that the dispersion relation for the magnons of planar N = 4 SYM can be identified with the Casimir of a certain deformation of the Poincaré algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between J an ..."
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It was recently noted that the dispersion relation for the magnons of planar N = 4 SYM can be identified with the Casimir of a certain deformation of the Poincaré algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between J and su(22) ⋉ R 2, we derive a qdeformed superPoincaré symmetry algebra of the kinematics. Using this, we show that the dynamic magnon representations may be obtained by boosting from a fixed restframe representation. We comment on aspects of the coalgebra structure and some implications for the question of boostcovariance of the Smatrix. 1 1
Semiclassical quantization of the giant magnon
 JHEP 06 (2007) 032, [arXiv:0704.2389 [hepth
"... Abstract: Solitons in field theory provide a window into regimes not directly accessible by the fundamental perturbative degrees of freedom. Motivated by interest in the worldsheet Smatrix of string theory in AdS5 ×S 5 in the limit of infinite worldsheet volume we consider the semiclassical quantiz ..."
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Abstract: Solitons in field theory provide a window into regimes not directly accessible by the fundamental perturbative degrees of freedom. Motivated by interest in the worldsheet Smatrix of string theory in AdS5 ×S 5 in the limit of infinite worldsheet volume we consider the semiclassical quantization of a particular soliton of this theory: the HofmanMaldacena ‘giant magnon ’ spinning string. We obtain explicit formulas for the complete spectrum of bosonic and fermionic fluctuations around the giant magnon. As an application of these results we confirm that the oneloop correction to the classical energy vanishes as expected. Contents
Nearflat space limit and Einstein manifolds
 JHEP 0802, 022 (2008) [arXiv:0707.1676 [hepth
"... We study the nearflat space limit for strings on AdS5 × M5, where the internal manifold M5 is equipped with a generic metric with U(1) 3 isometry. In the bosonic sector, the limiting sigma model is similar to the one found for AdS5 × S5, as the global symmetries are reduced in the most general case ..."
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We study the nearflat space limit for strings on AdS5 × M5, where the internal manifold M5 is equipped with a generic metric with U(1) 3 isometry. In the bosonic sector, the limiting sigma model is similar to the one found for AdS5 × S5, as the global symmetries are reduced in the most general case. When M5 is a SasakiEinstein space like T 1,1, Y p,q and L p,q,r, whose dual CFT’s have N = 1 supersymmetry, the nearflat space limit gives the same bosonic sector of the sigma model found for AdS5 ×S 5. This indicates the generic presence of integrable subsectors in Recent years have seen a deep progress in our understading of the spectrum of maximally supersymmetric AdS/CFT in four dimensions, namely the scaling dimensions of the N = 4 SYM and the energies for string states of the type IIB on AdS5 × S5 in the planar limit. On both sides of the correspondence, the problem is basically solved in
Anomalous dimensions of finite size field strength operators
 in N=4 SYM,” arXiv:0710.0217 [hepth
"... ABSTRACT: In the ��super YangMills theory, we consider the higher order anomalous dimensions �of purely gluonic operators Tr�where�is a component of the selfdual field strength. We propose compact closed expressions depending parametrically on that reproduce the prediction of Bethe Ansatz equation ..."
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ABSTRACT: In the ��super YangMills theory, we consider the higher order anomalous dimensions �of purely gluonic operators Tr�where�is a component of the selfdual field strength. We propose compact closed expressions depending parametrically on that reproduce the prediction of Bethe Ansatz equations up to five loop order, including transcendental dressing corrections. The size dependence follows a simple pattern as the perturbative order is increased and suggests hidden relations for these special operators. Contents
The AdS3 × S3 × S3 × S1 HernándezLópez phases: a semiclassical derivation
 J. Phys. A
"... QGaSLAB1305, arXiv:1306.5106 This note calculates the Hernández–López phases for strings in AdS3×S3×S3×S1 by semiclassical methods using the d(2, 1; α)2 algebraic curve. By working at general α we include modes absent from previous semiclassical calculations of this phase in AdS3×S3×T4, and in par ..."
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QGaSLAB1305, arXiv:1306.5106 This note calculates the Hernández–López phases for strings in AdS3×S3×S3×S1 by semiclassical methods using the d(2, 1; α)2 algebraic curve. By working at general α we include modes absent from previous semiclassical calculations of this phase in AdS3×S3×T4, and in particular can study the scattering of particles of different mass. By carefully rederiving the semiclassical formula we clarify some issues of antisymmetrisation, cutoffs and surface terms which could safely be ignored in AdS5×S5, and some issues about the terms c1,s which were absent there. As a result we see agreement with the recently calculated allloop dressing phase in the AdS3×S3×T4 case, and exactly 1/2 this in the general case AdS3×S3×S3×S1, for any α and any (light) polarisations. 1.
On String Smatrix, Bound States and TBA
, 2007
"... The study of finite J effects for the lightcone AdS5 × S5 superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The Smatrices describing t ..."
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The study of finite J effects for the lightcone AdS5 × S5 superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The Smatrices describing the scattering of physical excitations in the string and mirror models are related to each other by an analytic continuation. We show that the unitarity requirement for the mirror Smatrix fixes the Smatrices of both theories essentially uniquely. The resulting string Smatrix S(z1, z2) satisfies the generalized unitarity condition and, up to a scalar factor, is a meromorphic function on the elliptic curve associated to each variable z. The double Wick rotation is then accomplished by shifting the variables z by quarter of the imaginary period of the torus. We discuss the apparent bound states of the string and mirror models, and show that depending on a choice of the physical region there are one, two or 2M−1 solutions of the Mparticle bound state equations sharing the same conserved charges. For very large but finite values of J, most of these solutions, however, exhibit various signs of pathological behavior. In particular, they
FiniteSize Corrections of the CP 3 Giant Magnons: the Lüscher terms,” [arXiv:0810.0704
 in the SU(2) × SU(2) sector of AdS4 × CP 3 ,” [arXiv:0810.1246
"... We compute classical and first quantum finitesize corrections to the recently found giant magnon solutions in two different subspaces of CP 3. We use the Lüscher approach on the recently proposed exact Smatrix for N = 6 superconformal ChernSimons theory. We compare our results with the string and ..."
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We compute classical and first quantum finitesize corrections to the recently found giant magnon solutions in two different subspaces of CP 3. We use the Lüscher approach on the recently proposed exact Smatrix for N = 6 superconformal ChernSimons theory. We compare our results with the string and algebraic curve computations and find agreement, thus providing a nontrivial test for the new AdS4/CFT3 correspondence within an integrability framework. 1