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156
The AdS5 × S 5 superstring worldsheet Smatrix and crossing symmetry
, 2008
"... An Smatrix satisying the YangBaxter equation with symmetries relevant to the AdS5 × S 5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in thi ..."
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Cited by 226 (6 self)
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An Smatrix satisying the YangBaxter equation with symmetries relevant to the AdS5 × S 5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS5 ×S 5 superstring worldsheet Smatrix. We base our construction on a Hopfalgebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the Smatrix in the generalized rapidity plane.
The su(22) dynamic Smatrix
, 2005
"... We derive and investigate the Smatrix for the su(23) dynamic spin chain and for planar N = 4 super YangMills. Due to the large amount of residual symmetry in the excitation picture, the Smatrix turns out to be fully constrained up to an overall phase. We carry on by diagonalising it and obtain B ..."
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Cited by 219 (11 self)
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We derive and investigate the Smatrix for the su(23) dynamic spin chain and for planar N = 4 super YangMills. Due to the large amount of residual symmetry in the excitation picture, the Smatrix turns out to be fully constrained up to an overall phase. We carry on by diagonalising it and obtain Bethe equations for periodic states. This proves an earlier proposal for the asymptotic Bethe equations for the su(23) dynamic spin chain and for N = 4 SYM.
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 177 (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
The Analytic Bethe Ansatz for a Chain with Centrally Extended su(22) Symmetry
, 2006
"... We investigate the integrable structure of spin chain models with centrally extended su(22) and psu(2, 24) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the onedimensional Hubbard model as a special case. We begin with an overview of the repr ..."
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Cited by 140 (6 self)
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We investigate the integrable structure of spin chain models with centrally extended su(22) and psu(2, 24) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the onedimensional Hubbard model as a special case. We begin with an overview of the representation theory of centrally extended su(22). These results are applied in the construction and investigation of an interesting Smatrix with su(22) symmetry. In particular, they enable a remarkably simple proof of the YangBaxter relation. We also show the equivalence of the Smatrix to Shastry’s Rmatrix 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, 24) symmetry is sketched.
Quantum corrections to the string Bethe ansatz,” hepth/0603204
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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.
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 µterm 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 µterm 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 looporders 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 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 83 (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.
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 (4 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
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