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22
Giant magnons in AdS4/CFT3: dispersion, quantization and finite–size corrections,” hepth/0807.2861
"... We study giant magnon solutions in AdS4 × CP 3. We compute quantum corrections to their dispersion relation. We find out that the one–loop correction vanishes in infinite volume. This implies that the interpolating function h(λ) between strong and weak coupling regimes does not have a constant term ..."
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We study giant magnon solutions in AdS4 × CP 3. We compute quantum corrections to their dispersion relation. We find out that the one–loop correction vanishes in infinite volume. This implies that the interpolating function h(λ) between strong and weak coupling regimes does not have a constant term λ 0 at strong coupling. We also compute first nonvanishing finite volume correction to the one–loop expression. When compared to the Lüsher formula, our results could provide a nontrivial check of the AdS4 × CP 3 S–matrix proposed recently Nice example of integrable gauge theory is high–energy QCD [1, 2, 3]. Recently integrability was discovered for AdS5 × S 5 string theory [4, 5, 6, 7]. Many new applications of integrability arised together with famous Maldacena’s AdS/CFT duality [8]. Recently Aharony, Bergman, Jafferis and Maldacena [9] proposed duality of AdS4 × CP 3 and
Algebraic Curves for Integrable String Backgrounds,” arXiv:1005.1342 [hepth
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Z.Tsuboi, Baxter’s Qoperators and operatorial Bäcklund flow for quantum (super)spin chains
 Commun. Math. Phys
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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 integrability  A journey through the twodimensional hidden symmetries in the AdS/CFT dualities
, 2010
"... One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in th ..."
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One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in twodimensional σmodels and in the AdS/CFT context. The first part is focused on the AdS5/CFT4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS5 × S5 are discussed in both pure spinor and GreenSchwarz formulations. The second part is dedicated to the AdS4/CFT3 duality with particular attention to the type IIA superstring on AdS4 × CP 3 and its integrability. This review is based on a shortened and revised version of the author’s PhD thesis, discussed at Uppsala University in September 2009.
Integrability of the Gauged Linear Sigma Model for
, 804
"... Recently, a gauged linear sigma model was proposed by Berkovits and Vafa which can be used to describe the AdS5 × S 5 superstring at finite and zero radius. In this paper we show that the model is classically integrable by constructing its first nonlocal conserved charge and a superspace Lax “quart ..."
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Recently, a gauged linear sigma model was proposed by Berkovits and Vafa which can be used to describe the AdS5 × S 5 superstring at finite and zero radius. In this paper we show that the model is classically integrable by constructing its first nonlocal conserved charge and a superspace Lax “quartet”. Quantum conservation of the nonlocal charge follows easily from superspace rules. 1
Firstprinciples derivation of the AdS/CFT Ysystems
 Journal of High Energy Physics
, 2011
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Worldsheet spectrum in AdS4/CFT3 correspondence
, 903
"... The AdS4/CFT3 duality is a new example of an integrable and exactly solvable AdS/CFT system. There is, however, a puzzling mismatch between the number of degrees of freedom used in the exact solution (4B + 4F scattering states) and 8B + 8F transverse oscillation modes of critical superstring theory. ..."
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The AdS4/CFT3 duality is a new example of an integrable and exactly solvable AdS/CFT system. There is, however, a puzzling mismatch between the number of degrees of freedom used in the exact solution (4B + 4F scattering states) and 8B + 8F transverse oscillation modes of critical superstring theory. We offer a resolution of this puzzle by arguing that half of the string modes dissolve in the continuum of twoparticle states once α ′ corrections are taken into account. We also check that the conjectured exact Smatrix of AdS4/CFT3 [1] agrees with the treelevel worldsheet calculation. A new example of the AdS4/CFT3 duality proposed in [2] and further developed in [3] establishes an equivalence of the superconformal ChernSimonsmatter theory and type IIA string theory on AdS4×CP 3 [4–6]. This AdS/CFT system turns out to be integrable [7,4,5,8] and exactly solvable [9,1,10] in the largeN (free string) limit. However, certain