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281
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 228 (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 222 (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 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
Wrapping interactions and a new source of corrections to the spinchain/string duality
, 2006
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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 143 (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.
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.
Connecting giant magnons to the ppwave: An interpolating limit
 of AdS5×S 5 ” [hepth/0612079
"... We consider a particular largeradius limit of the worldsheet Smatrix for strings propagating on AdS5 × S 5. This limiting theory interpolates smoothly between the socalled planewave and giantmagnon 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 largeradius limit of the worldsheet Smatrix for strings propagating on AdS5 × S 5. This limiting theory interpolates smoothly between the socalled planewave and giantmagnon 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 nontrivial, 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 giantmagnon region. In addition, we rely on general considerations to draw some basic conclusions about the analytic structure of the S matrix
Longrange psu(2, 24) Bethe Ansätze for Gauge Theory and Strings
, 2005
"... We generalize various existing higherloop Bethe ansätze for simple sectors of the integrable longrange dynamic spin chain describing planar N = 4 Super YangMills Theory to the full psu(2, 24) symmetry and, asymptotically, to arbitrary loop order. We perform a large number of tests of our conject ..."
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Cited by 86 (5 self)
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We generalize various existing higherloop Bethe ansätze for simple sectors of the integrable longrange dynamic spin chain describing planar N = 4 Super YangMills Theory to the full psu(2, 24) symmetry and, asymptotically, to arbitrary loop order. We perform a large number of tests of our conjectured equations, such as internal consistency, comparison to direct threeloop diagonalization and expected thermodynamic behavior. In the special case of the su(12) subsector, corresponding to a longrange tJ model, we are able to derive, up to three loops, the Smatrix and the associated nested Bethe ansatz from the gauge theory dilatation operator. We conjecture novel allorder Smatrices for the su(12) and psu(1, 12) subsectors, and show that they satisfy the YangBaxter equation. Throughout the paper, we muse about the idea that quantum string theory on AdS5 × S 5 is also described by a psu(2, 24) spin chain. We propose asymptotic allorder Bethe equations for this
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