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143
Transcendentality and crossing
, 2006
"... We discuss possible phase factors for the Smatrix of planar N = 4 gauge theory, leading to modifications at fourloop order as compared to an earlier proposal. While these result in a fourloop breakdown of perturbative BMNscaling, KotikovLipatov transcendentality in the universal scaling function ..."
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Cited by 175 (2 self)
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We discuss possible phase factors for the Smatrix of planar N = 4 gauge theory, leading to modifications at fourloop order as compared to an earlier proposal. While these result in a fourloop breakdown of perturbative BMNscaling, KotikovLipatov transcendentality in the universal scaling function for largespin 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 nonperturbatively related to a recently conjectured crossingsymmetric phase factor for perturbative string theory on AdS5 × S 5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve
Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
, 2009
"... Moving from the mirror theory BetheYang equations proposed by Arutynov and Frolov, we derive the Thermodynamic Bethe Ansatz equations which should control the spectrum of the planar AdS5/CFT4 correspondence. The associated set of universal functional relations (Ysystem) satisfied by the exponentia ..."
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Cited by 127 (5 self)
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Moving from the mirror theory BetheYang equations proposed by Arutynov and Frolov, we derive the Thermodynamic Bethe Ansatz equations which should control the spectrum of the planar AdS5/CFT4 correspondence. The associated set of universal functional relations (Ysystem) satisfied by the exponentials of the TBA pseudoenergies is deduced, confirming the structure inferred by Gromov, Kazakov and Vieira.
On the integrability of Wilson loops
 in AdS5 × S5: Some periodic ansätze,” JHEP 01 (2006) 056, hepth/0506058
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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.
Konishi operator at intermediate coupling
 J. Phys. A44
"... Abstract: TBA equations for twoparticle states from the sl(2) sector proposed by Arutyunov, Suzuki and the author are solved numerically for the Konishi operator descendent up to ’t Hooft’s coupling λ ≈ 2046. The data obtained is used to analyze the properties of Yfunctions and address the issue o ..."
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Cited by 29 (1 self)
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Abstract: TBA equations for twoparticle states from the sl(2) sector proposed by Arutyunov, Suzuki and the author are solved numerically for the Konishi operator descendent up to ’t Hooft’s coupling λ ≈ 2046. The data obtained is used to analyze the properties of Yfunctions and address the issue of the existence of the critical values of the coupling. In addition we find a new integral representation for the BES dressing phase which substantially reduces the computational time.
From Characters to Quantum (Super)Spin Chains via Fusion
, 2007
"... We give an elementary proof of the BazhanovReshetikhin determinant formula for rational transfer matrices of the twisted quantum superspin chains associated with the gl(KM) algebra. This formula describes the most general fusion of transfer matrices in symmetric representations into arbitrary fin ..."
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Cited by 24 (3 self)
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We give an elementary proof of the BazhanovReshetikhin determinant formula for rational transfer matrices of the twisted quantum superspin chains associated with the gl(KM) algebra. This formula describes the most general fusion of transfer matrices in symmetric representations into arbitrary finite dimensional representations of the algebra and is at the heart of analytical Bethe ansatz approach. Our technique represents a systematic generalization of the usual JacobiTrudi formula for characters to its quantum analogue using certain group derivatives.
Solutions of the Tsystem and Baxter equations for supersymmetric spin chains”, arXiv:0906.2039
"... We propose Wronskianlike determinant formulae for the Baxter Qfunctions and the eigenvalues of transfer matrices for spin chains related to the quantum affine superalgebra Uq ( ̂ gl(MN)). In contrast to the supersymmetric BazhanovReshetikhin formula (the quantum supersymmetric JacobiTrudi form ..."
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Cited by 18 (4 self)
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We propose Wronskianlike determinant formulae for the Baxter Qfunctions and the eigenvalues of transfer matrices for spin chains related to the quantum affine superalgebra Uq ( ̂ gl(MN)). In contrast to the supersymmetric BazhanovReshetikhin formula (the quantum supersymmetric JacobiTrudi formula) proposed in [Z. Tsuboi, J. Phys. A: Math. Gen. 30 (1997) 7975], the size of the matrices of these Wronskianlike formulae is less than or equal to M + N. Base on these formulae, we give new expressions of the solutions of the Tsystem (fusion relations for transfer matrices) for supersymmetric spin chains proposed in the abovementioned paper. Baxter equations also follow from the Wronskianlike formulae. They are finite order linear difference equations with respect to the Baxter Qfunctions. Moreover, the Wronskianlike formulae also explicitly solve the functional relations for Bäcklund flows proposed in [V. Kazakov, A. Sorin,