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14
Finite size giant magnons in the SU(2) × SU(2) sector of AdS4 ×�
, 810
"... We use the algebraic curve and Lüscher’s µterm to calculate the leading order finite size corrections to the dispersion relation of giant magnons in the SU(2) × SU(2) sector of AdS4 ×�3. We consider a single magnon as well as one magnon in each SU(2). In addition the algebraic curve computation is ..."
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We use the algebraic curve and Lüscher’s µterm to calculate the leading order finite size corrections to the dispersion relation of giant magnons in the SU(2) × SU(2) sector of AdS4 ×�3. We consider a single magnon as well as one magnon in each SU(2). In addition the algebraic curve computation is generalized to give the leading order correction for an arbitrary multimagnon state in the SU(2) × SU(2) sector. Contents 1
Nbody Dynamics of Giant Magnons in R × S²
, 2008
"... We pursue the question of multimagnon dynamics, focusing on the simplest case of magnons moving on R × S² and working at the semiclassical level. Through a Pohlmeyer reduction, the problem reduces to another well known integrable field theory, the sineGordon model, which can be exactly described t ..."
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We pursue the question of multimagnon dynamics, focusing on the simplest case of magnons moving on R × S² and working at the semiclassical level. Through a Pohlmeyer reduction, the problem reduces to another well known integrable field theory, the sineGordon model, which can be exactly described through an Nbody model of Calogero type. The two theories coincide at the level of equations of motion, but physical quantities like the energies (of magnons and solitons) and the associated phase shifts are different. We start from the equivalence of the two systems at the level of equations of motion and require that the new (string theory) model reproduces the correct magnon energies and the phase shift, both of which differ from the soliton case. From the comparison of energies we suggest a Hamiltonian, and from requiring the correct phase shift we are led to a nontrivial Poisson structure representing the magnons.
The Bound State SMatrix for AdS5 × S 5 Superstring
, 902
"... Abstract: We determine the Smatrix that describes scattering of arbitrary bound states in the lightcone string theory in AdS5 × S 5. The corresponding construction relies on the Yangian symmetry and the superspace formalism for the bound state representations. The basic analytic structure supporti ..."
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Abstract: We determine the Smatrix that describes scattering of arbitrary bound states in the lightcone string theory in AdS5 × S 5. The corresponding construction relies on the Yangian symmetry and the superspace formalism for the bound state representations. The basic analytic structure supporting the Smatrix entries turns out to be the hypergeometric function 4F3. We show that for particular bound state numbers it reproduces all the scattering matrices previously obtained in the literature. Our findings should be relevant for the TBA and Lüscher approaches to the finitesize spectral problem. They also shed some light on the construction of the universal Rmatrix for the centrallyextended psu(22)
ImperialTPRR01/2009 Notes on supersymmetric Wilson loops on a twosphere
, 905
"... We study a recently discovered family of 1/8BPS supersymmetric Wilson loops in N = 4 super YangMills theory and their string theory duals. The operators are defined for arbitrary contours on a twosphere in spacetime, and they were conjectured to be captured perturbatively by 2d bosonic YangMill ..."
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We study a recently discovered family of 1/8BPS supersymmetric Wilson loops in N = 4 super YangMills theory and their string theory duals. The operators are defined for arbitrary contours on a twosphere in spacetime, and they were conjectured to be captured perturbatively by 2d bosonic YangMills theory. In the AdS dual, they are described by pseudoholomorphic string surfaces living on a certain submanifold of AdS5 × S 5. We show that the regularized area of these string surfaces is invariant under area preserving diffeomorphisms of the boundary loop, in agreement with the conjecture. Further, we find a connection between the pseudoholomorphicity equations and an auxiliary σmodel on S 3, which may help to construct new 1/8BPS string solutions. We also show that the conjectured relation to 2d YangMills implies that a connected correlator of two Wilson loops is computed by a Hermitian Gaussian twomatrix model. On the AdS dual side, we argue that the connected correlator is described by two disconnected disks interacting through the exchange of supergravity modes, and
ITEPTH17/09 ImperialTPRR01/2009
, 905
"... Notes on supersymmetric Wilson loops ..."
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UT08 22 FiniteSize Effects for MultiMagnon States
, 807
"... We propose the generalized Lüscher formula for multimagnon states, and show that it correctly reproduces the finitesize correction to the energy of multi giant magnons at classical and oneloop levels. We also show that the µterm formula, which corresponds to the classical string energy, is consi ..."
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We propose the generalized Lüscher formula for multimagnon states, and show that it correctly reproduces the finitesize correction to the energy of multi giant magnons at classical and oneloop levels. We also show that the µterm formula, which corresponds to the classical string energy, is consistent with the finitesize correction from the Bethe Ansatz Equations in the su(2) sector. Finally, we evaluate our formula at weak coupling under some approximations, and find that the transcendental terms arise from a sum over an infinite tower of BPS boundstates. a
arXiv:0811.2423 Giant Magnons in AdS4×CP 3: Embeddings, Charges and a Hamiltonian
, 2008
"... This paper studies giant magnons in CP 3, which in all known cases are old solutions from S 5 placed into two and threedimensional subspaces of CP 3, namely CP 1, RP 2 and RP 3. We clarify some points about these subspaces, and other potentially interesting three and fourdimensional subspaces. A ..."
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This paper studies giant magnons in CP 3, which in all known cases are old solutions from S 5 placed into two and threedimensional subspaces of CP 3, namely CP 1, RP 2 and RP 3. We clarify some points about these subspaces, and other potentially interesting three and fourdimensional subspaces. After confirming that ∆ − (J1 − J4)/2 is a Hamiltonian for small fluctuations of the relevant ‘vacuum’ point particle solution, we use it to calculate the dispersion relation of each of the inequivalent giant magnons. We comment on the embedding of finiteJ solutions, and use these to compare string solutions to giant magnons in the algebraic curve. 1