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104
The factorized Smatrix of CFT/AdS
 JHEP
, 2005
"... Abstract: We argue that the recently discovered integrability in the largeN CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s ..."
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Cited by 239 (7 self)
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Abstract: We argue that the recently discovered integrability in the largeN CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s dilatation operator nor the string sigma model’s quantum Hamiltonian, but instead the respective factorized Smatrix. To illustrate the idea, we focus on the closed fermionic su(11) sector of the N = 4 gauge theory. We introduce a new technique, the perturbative asymptotic Bethe ansatz, and use it to extract this sector’s threeloop Smatrix from Beisert’s involved algebraic work on the threeloop su(23) sector. We then show that the current knowledge about semiclassical and nearplanewave quantum strings in the su(2), su(11) and sl(2) sectors of AdS5 ×S 5 is fully consistent with the existence of a factorized Smatrix. Analyzing the available information, we find an intriguing relation between the three associated Smatrices. Assuming that the relation also holds in gauge theory, we derive the threeloop Smatrix of the sl(2) sector even though this sector’s dilatation operator is not yet known beyond one loop. The resulting
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.
Wrapping interactions and a new source of corrections to the spinchain/string duality
, 2006
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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 (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
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
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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Cited by 48 (0 self)
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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
An action variable of the sineGordon model
 J. Geom. Phys
"... It was conjectured that the classical bosonic string in AdS times a sphere has a special action variable which corresponds to the length of the operator on the field theory side. We discuss the analogous action variable in the sineGordon model. We explain the relation between this action variable a ..."
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Cited by 17 (0 self)
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It was conjectured that the classical bosonic string in AdS times a sphere has a special action variable which corresponds to the length of the operator on the field theory side. We discuss the analogous action variable in the sineGordon model. We explain the relation between this action variable and the Bäcklund transformations and show that the corresponding hidden symmetry acts on breathers by shifting their phase. It can be considered a nonlinear analogue of splitting the solution of the free field equations into the positive and negativefrequency part. 1 Introduction. Studies of classical strings in AdS5 × S 5 was an important part of the recent work on the AdS/CFT correspondence. It was observed that the energies of the fast moving classical strings reproduce the anomalous dimension of the field theory operators with the large Rcharge, at least in the first and
Dilatation operator and the super YangMills duals of open strings on AdS giant gravitons
, 2006
"... We study the oneloop anomalous dimensions of the Super YangMills dual operators to open strings ending on AdS giant gravitons. AdS giant gravitons have no upper bound for their angular momentum and we represent them by the contraction of scalar fields, carrying the appropriate Rcharge, with a t ..."
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Cited by 15 (1 self)
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We study the oneloop anomalous dimensions of the Super YangMills dual operators to open strings ending on AdS giant gravitons. AdS giant gravitons have no upper bound for their angular momentum and we represent them by the contraction of scalar fields, carrying the appropriate Rcharge, with a totally symmetric tensor. We represent the open string motion along AdS directions by appending to the giant graviton operator a product of fields including covariant derivatives. We derive a bosonic lattice Hamiltonian that describes the mixing of these excited AdS giants operators under the action of the oneloop dilatation operator of N = 4 SYM. This Hamiltonian captures several intuitive differences with respect to the case of sphere giant gravitons. A semiclassical analysis of the Hamiltonian allows us to give a geometrical interpretation for the labeling used to describe the fields products appended to the AdS giant operators. It also allows us to show evidence for the existence of continuous bands in the Hamiltonian spectrum.
Semiclassical strings in LuninMaldacena background
"... The aim of this paper is to investigate semiclassical rotating string configurations in the recently found LuninMaldacena background. This background is conjectured to be dual to the LeighStrassler βdeformation of N = 4 SYM and therefore a good laboratory for tests of the AdS/CFT correspondence b ..."
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Cited by 10 (2 self)
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The aim of this paper is to investigate semiclassical rotating string configurations in the recently found LuninMaldacena background. This background is conjectured to be dual to the LeighStrassler βdeformation of N = 4 SYM and therefore a good laboratory for tests of the AdS/CFT correspondence beyond the well explored AdS5 × S 5 case. We consider different multispin configurations of rotating strings by allowing the strings to move in both the AdS5 and the deformed S 5 part of the LuninMaldacena background. For all of these configurations we compute the string energy in terms of the angular momenta and the string winding numbers and thus provide the possibility of comparing our results to the anomalous dimension of the corresponding dilatation operator. 1