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240
Integrability for the Full Spectrum of Planar AdS/CFT II
, 2009
"... Using the thermodynamical Bethe ansatz method we derive an infinite set of integral nonlinear equations for the spectrum of states/operators in AdS/CFT. The Ysystem conjectured in [1] for the spectrum of all operators in planar N = 4 SYM theory follow from these equations. In particular, we present ..."
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Cited by 84 (4 self)
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Using the thermodynamical Bethe ansatz method we derive an infinite set of integral nonlinear equations for the spectrum of states/operators in AdS/CFT. The Ysystem conjectured in [1] for the spectrum of all operators in planar N = 4 SYM theory follow from these equations. In particular, we present the integral equations for the spectrum of all operators within the sl(2) sector.
Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric YangMills Theory
, 2009
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Finitesize Effects from Giant Magnons
, 2006
"... In order to analyze finitesize effects for the gaugefixed string sigma model on AdS5 × S 5, we construct onesoliton solutions carrying finite angular momentum J. In the infinite J limit the solutions reduce to the recently constructed onemagnon configuration of Hofman and Maldacena. The solution ..."
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Cited by 58 (5 self)
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In order to analyze finitesize effects for the gaugefixed string sigma model on AdS5 × S 5, we construct onesoliton solutions carrying finite angular momentum J. In the infinite J limit the solutions reduce to the recently constructed onemagnon configuration of Hofman and Maldacena. The solutions do not satisfy the levelmatching condition and hence exhibit a dependence on the gauge choice, which however disappears as the size J is taken to infinity. Interestingly, the solutions do not conserve all the global charges of the psu(2, 24) algebra of the sigma model, implying that the symmetry algebra of the gaugefixed string sigma model is different from psu(2, 24) for finite J, once one gives up the levelmatching condition. The magnon dispersion relation exhibits exponential corrections with respect to the infinite J solution. We also find a generalisation of our onemagnon configuration to a solution carrying two charges on the sphere. We comment on the possible implications of our findings for the existence of the Bethe ansatz describing the spectrum
Bethe Ansatz for a Quantum Supercoset Sigma Model
, 2005
"... We study an integrable conformal OSp(2m + 22m) supercoset model as an analog to the AdS5 × S 5 superstring worldsheet theory. Using the known Smatrix for this system, we obtain integral equations for states of large particle number in an SU(2) sector, which are exact in the sigma model coupling c ..."
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Cited by 55 (0 self)
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We study an integrable conformal OSp(2m + 22m) supercoset model as an analog to the AdS5 × S 5 superstring worldsheet theory. Using the known Smatrix for this system, we obtain integral equations for states of large particle number in an SU(2) sector, which are exact in the sigma model coupling constant. As a check, we derive as a limit the general classical Bethe equation of Kazakov, Marshakov, Minahan, and Zarembo. There are two distinct quantum expansions around the wellstudied classical limit, the λ −1/2 effects and the 1/J effects. Our approach captures the first type, but
Exact expressions for quantum corrections to spinning strings,” Phys
 Lett. B
"... sakura.schafernameki at desy.de The oneloop worldsheet quantum corrections to the energy of spinning strings on R×S 3 within AdS5 × S 5 are reexamined. The explicit expansion in the effective ’t Hooft coupling λ ′ = λ/J 2 is rigorously derived. The expansion contains both analytic and nonanalyti ..."
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Cited by 46 (0 self)
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sakura.schafernameki at desy.de The oneloop worldsheet quantum corrections to the energy of spinning strings on R×S 3 within AdS5 × S 5 are reexamined. The explicit expansion in the effective ’t Hooft coupling λ ′ = λ/J 2 is rigorously derived. The expansion contains both analytic and nonanalytic terms in λ ′ , as well as exponential corrections. Furthermore, we pin down the origin of the terms that are not captured by the quantum string Bethe ansatz, which only produces analytic terms in λ ′. It is shown that the analytic terms arise from string fluctuations within the S 3, whereas the nonanalytic and exponential terms, which are not captured by the Bethe ansatz, originate from the fluctuations in all directions within the supersymmetric sigma model on AdS5 × S 5. We also comment on the case of spinning string in AdS3 × S 1.1 Introduction and Summary The worldsheet oneloop corrections to the energy of spinning strings in AdS5 × S5 has been the subject of vivid discussions. A better understanding of these quantum string corrections would not only elucidate various aspects of the AdS/CFT correspondence between string theory on AdS5 × S5 and d = 4, N = 4 SU(Nc) SYM theory, but would moreover provide valuable
Quantum Deformations of the OneDimensional Hubbard Model
, 802
"... The centrally extended superalgebra psu(22) ⋉ R 3 was shown to play an important role for the integrable structures of the onedimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation Uq(psu(22)⋉R 3) and derive the fundamental Rmatrix. From the ..."
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Cited by 35 (0 self)
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The centrally extended superalgebra psu(22) ⋉ R 3 was shown to play an important role for the integrable structures of the onedimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation Uq(psu(22)⋉R 3) and derive the fundamental Rmatrix. From the latter we deduce an integrable spin chain Hamiltonian with three independent parameters and the corresponding Bethe equations to describe the spectrum on periodic chains. We relate our Hamiltonian to a twoparametric Hamiltonian proposed by Alcaraz and Bariev which can be considered a quantum deformation of the onedimensional Hubbard model. 1 Introduction and Overview Finding the spectrum of a quantum mechanical model is an intricate problem. Indeed, for generic models there is no complete analytic solution to the spectrum essentially because nonlinear interaction terms in the Hamiltonian easily make the problem chaotic and intractable. Only very few models, such as the harmonic oscillator, are solvable exactly.
N = 4 SYM to Two Loops: Compact Expressions for the NonCompact Symmetry Algebra of the su(1, 12) Sector
, 2005
"... We begin a study of higherloop corrections to the dilatation generator of N = 4 SYM in noncompact sectors. In these sectors, the dilatation generator contains infinitely many interactions, and therefore one expects very complicated higherloop corrections. Remarkably, we find a short and simple ex ..."
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Cited by 34 (5 self)
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We begin a study of higherloop corrections to the dilatation generator of N = 4 SYM in noncompact sectors. In these sectors, the dilatation generator contains infinitely many interactions, and therefore one expects very complicated higherloop corrections. Remarkably, we find a short and simple expression for the twoloop dilatation generator. Our solution for the noncompact su(1,12) sector consists of nested commutators of four O(g 1) generators and one simple auxiliary generator. Moreover, the solution does not require the planar limit; we conjecture that it is valid for any gauge group. To obtain the twoloop dilatation generator, we find the complete O(g 3) symmetry algebra for this sector, which is also given by concise expressions. We check our solution using published results of direct field theory calculations. By applying the expression for the twoloop dilatation generator to compute selected anomalous dimensions and the sl(2) sector internal Smatrix, we confirm recent conjectures of the higherloop Bethe ansatz of
Bethe ansatz in stringy sigma models
"... We compute the exact Smatrix and give the Bethe ansatz solution for three sigmamodels which arise as subsectors of string theory in AdS5×S 5: LandauLifshitz model (nonrelativistic sigmamodel on S 2), AldayArutyunovFrolov model (fermionic sigmamodel with su(11) symmetry), and FaddeevResheti ..."
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Cited by 29 (3 self)
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We compute the exact Smatrix and give the Bethe ansatz solution for three sigmamodels which arise as subsectors of string theory in AdS5×S 5: LandauLifshitz model (nonrelativistic sigmamodel on S 2), AldayArutyunovFrolov model (fermionic sigmamodel with su(11) symmetry), and FaddeevReshetikhin model (string sigmamodel on S 3 × R).
A new derivation of Luscher Fterm and fluctuations around the giant magnon
 JHEP 0806 (2008) 036 [arXiv:0801.4463 [hepth
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