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130
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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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
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.
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
Magnon boundstate scattering in gauge and string theory”, hepth/0608049
"... It has been shown that, in the infinite length limit, the magnons of the gauge theory spin chain can form bound states carrying one finite and one strictly infinite Rcharge. These bound states have been argued to be associated to simple poles of the multiparticle scattering matrix and to world she ..."
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It has been shown that, in the infinite length limit, the magnons of the gauge theory spin chain can form bound states carrying one finite and one strictly infinite Rcharge. These bound states have been argued to be associated to simple poles of the multiparticle scattering matrix and to world sheet solitons carrying the same charges. Classically, they can be mapped to the solitons of the complex sineGordon theory. Under relatively general assumptions we derive the condition that simple poles of the twoparticle scattering matrix correspond to physical bound states and construct higher bound states “one magnon at a time”. We construct the scattering matrix of the bound states of the BDS and the AFS Smatrices. The bound state Smatrix exhibits simple and double poles and thus its analytic structure is much richer than that of the elementary magnon Smatrix. We also discuss the bound states appearing in larger sectors and their Smatrices. The large ’t Hooft coupling limit of the scattering phase of the bound states in the SU(2) sector is found to agree with the semiclassical scattering of world sheet solitons. Intriguingly, the contribution of the dressing phase has an independent world sheet interpretation as the solitonantisoliton scattering phase shift. The small momentum limit provides independent tests of these identifications. 1 1
Spinning superstrings at two loops: strongcoupling corrections to dimensions of largetwist SYM operators
, 2007
"... ..."
A new derivation of Luscher Fterm and fluctuations around the giant magnon
 JHEP 0806 (2008) 036 [arXiv:0801.4463 [hepth
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Nesting and dressing
"... We compute the anomalous dimensions of field strength operators Tr F L in N = 4 SYM from an asymptotic nested Bethe ansatz to allloop order. Starting from the exact solution of the oneloop problem at arbitrary L, we derive a single effective integral equation for the thermodynamic L → ∞ limit of ..."
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We compute the anomalous dimensions of field strength operators Tr F L in N = 4 SYM from an asymptotic nested Bethe ansatz to allloop order. Starting from the exact solution of the oneloop problem at arbitrary L, we derive a single effective integral equation for the thermodynamic L → ∞ limit of these dimensions. We also include the recently proposed phase factor for the Smatrix of the planar AdS/CFT system. The terms in the effective equation corresponding to, respectively, the nesting and the dressing are structurally very similar. This hints at the physical origin of the dressing phase, which we conjecture to arise from the hidden presence of infinitely many auxiliary Bethe roots describing a nontrivial “filled ” structure of the theory’s BPS vacuum. We finally show that the mechanism for creating effective nesting/dressing kernels is quite generic by also deriving the integral equation for the allloop dimension of a certain oneloop so(6) singlet state. 1 Motivation, Conclusion and Overview There is much evidence that planar N = 4 SYM theory is integrable and that its spectral problem is therefore exactly solvable. It was shown by Minahan and Zarembo that the dilatation operator in the scalar matter sector at one loop can be mapped to the Hamiltonian