Results 1  10
of
155
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
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.
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
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 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 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.
Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric YangMills Theory
, 2009
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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
Giant magnons in AdS4/CFT3: dispersion, quantization and finite–size corrections,” hepth/0807.2861
"... We study giant magnon solutions in AdS4 × CP 3. We compute quantum corrections to their dispersion relation. We find out that the one–loop correction vanishes in infinite volume. This implies that the interpolating function h(λ) between strong and weak coupling regimes does not have a constant term ..."
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Cited by 37 (0 self)
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We study giant magnon solutions in AdS4 × CP 3. We compute quantum corrections to their dispersion relation. We find out that the one–loop correction vanishes in infinite volume. This implies that the interpolating function h(λ) between strong and weak coupling regimes does not have a constant term λ 0 at strong coupling. We also compute first nonvanishing finite volume correction to the one–loop expression. When compared to the Lüsher formula, our results could provide a nontrivial check of the AdS4 × CP 3 S–matrix proposed recently Nice example of integrable gauge theory is high–energy QCD [1, 2, 3]. Recently integrability was discovered for AdS5 × S 5 string theory [4, 5, 6, 7]. Many new applications of integrability arised together with famous Maldacena’s AdS/CFT duality [8]. Recently Aharony, Bergman, Jafferis and Maldacena [9] proposed duality of AdS4 × CP 3 and
Rashkov, “MagnonLike Dispersion Relation from Mtheory,” [hepth/0607116
"... We investigate classical rotating membranes in two different backgrounds. First, we obtain membrane solution in AdS4 × S 7 background, analogous to the solution obtained by Hofman and Maldacena in the case of string theory. We find a magnon type dispersion relation similar to that of Hofman and Mald ..."
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Cited by 24 (7 self)
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We investigate classical rotating membranes in two different backgrounds. First, we obtain membrane solution in AdS4 × S 7 background, analogous to the solution obtained by Hofman and Maldacena in the case of string theory. We find a magnon type dispersion relation similar to that of Hofman and Maldacena and to the one found by Dorey for the two spin case. In the appendix of the paper, we consider membrane solutions in AdS7 × S 4, which give new relations between the conserved charges. Keywords: Mtheory, AdSCFT correspondence, spin chains. 1