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228
Transcendentality and crossing
, 2006
"... 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 BMNscaling, Kotikov-Lipatov 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 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 BMNscaling, 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 AdS5 × S 5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve
The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
, 2006
"... We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2, 2|4) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the one-dimensional Hubbard model as a special case. We begin with an overview of the repr ..."
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Cited by 143 (6 self)
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We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2, 2|4) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the one-dimensional Hubbard model as a special case. We begin with an overview of the representation theory of centrally extended su(2|2). These results are applied in the construction and investigation of an interesting S-matrix with su(2|2) symmetry. In particular, they enable a remarkably simple proof of the Yang-Baxter relation. We also show the equivalence of the S-matrix to Shastry’s R-matrix and thus uncover a hidden supersymmetry in the integrable structure of the Hubbard model. We then construct eigenvalues of the corresponding transfer matrix in order to formulate an analytic Bethe ansatz. Finally, the form of transfer matrix eigenvalues for models with psu(2, 2|4) symmetry is sketched.
Connecting giant magnons to the pp-wave: An interpolating limit
- of AdS5×S 5 ” [hep-th/0612079
"... We consider a particular large-radius limit of the worldsheet S-matrix for strings propagating on AdS5 × S 5. This limiting theory interpolates smoothly between the so-called plane-wave and giant-magnon regimes of the theory. The sigma model in this region simplifies; it stands as a toy model of the ..."
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Cited by 92 (0 self)
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We consider a particular large-radius limit of the worldsheet S-matrix for strings propagating on AdS5 × S 5. This limiting theory interpolates smoothly between the so-called plane-wave and giant-magnon regimes of the theory. The sigma model in this region simplifies; it stands as a toy model of the full theory, and may be easier to solve directly. The S matrix of the limiting theory is non-trivial, and receives contributions to all orders in the α ′ expansion. We analyze a guess for the full worldsheet S matrix that was formulated recently by Beisert, Hernandez and Lopez, and Beisert, Eden, and Staudacher, and take the corresponding limit. After doing a Borel resummation we find that the proposed S matrix reproduces the expected results in the giant-magnon region. In addition, we rely on general considerations to draw some basic conclusions about the analytic structure of the S matrix
Wrapping interactions at strong coupling – the giant magnon
, 2008
"... We derive generalized Lüscher formulas for finite size corrections in a theory with a general dispersion relation. For the AdS5 × S⁵ superstring these formulas encode leading wrapping interaction effects. We apply the generalized µ-term formula to calculate finite size corrections to the dispersion ..."
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Cited by 90 (3 self)
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We derive generalized Lüscher formulas for finite size corrections in a theory with a general dispersion relation. For the AdS5 × S⁵ superstring these formulas encode leading wrapping interaction effects. We apply the generalized µ-term formula to calculate finite size corrections to the dispersion relation of the giant magnon at strong coupling. The result exactly agrees with the classical string computation of Arutyunov, Frolov and Zamaklar. The agreement involved a Borel resummation of all even loop-orders of the BES/BHL dressing factor thus providing a strong consistency check for the choice of the dressing factor.
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 Y-system 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 Y-system 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 Yang-Mills Theory
, 2009
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Finite-size Effects from Giant Magnons
, 2006
"... In order to analyze finite-size effects for the gauge-fixed string sigma model on AdS5 × S 5, we construct one-soliton solutions carrying finite angular momentum J. In the infinite J limit the solutions reduce to the recently constructed one-magnon configuration of Hofman and Maldacena. The solution ..."
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Cited by 58 (5 self)
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In order to analyze finite-size effects for the gauge-fixed string sigma model on AdS5 × S 5, we construct one-soliton solutions carrying finite angular momentum J. In the infinite J limit the solutions reduce to the recently constructed one-magnon 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, 2|4) algebra of the sigma model, implying that the symmetry algebra of the gauge-fixed string sigma model is different from psu(2, 2|4) for finite J, once one gives up the level-matching condition. The magnon dispersion relation exhibits exponential corrections with respect to the infinite J solution. We also find a generalisation of our one-magnon 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
On the integrability of Wilson loops
- in AdS5 × S5: Some periodic ansätze,” JHEP 01 (2006) 056, hep-th/0506058
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Quantum Deformations of the One-Dimensional Hubbard Model
, 802
"... The centrally extended superalgebra psu(2|2) ⋉ R 3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation Uq(psu(2|2)⋉R 3) and derive the fundamental R-matrix. From the ..."
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Cited by 35 (0 self)
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The centrally extended superalgebra psu(2|2) ⋉ R 3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation Uq(psu(2|2)⋉R 3) and derive the fundamental R-matrix. 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 two-parametric Hamiltonian proposed by Alcaraz and Bariev which can be considered a quantum deformation of the one-dimensional 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 non-linear interaction terms in the Hamiltonian easily make the problem chaotic and intractable. Only very few models, such as the harmonic oscillator, are solvable exactly.
