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Giant Magnon and Spike Solutions with Two Spins
 in AdS4 × CP 3 ,” JHEP 0811, 084 (2008) [arXiv:0809.5106 [hepth]] • D. Bombardelli and D. Fioravanti, “FiniteSize Corrections of the CP 3 Giant Magnons: the Lüscher terms,” arXiv:0810.0704 [hepth
, 2008
"... In the string theory in AdS4 × CP 3 we construct the giant magnon and spike solutions with two spins in two kinds of subspaces of Rt×CP 3 and derive the dispersion relations for them. For the single giant magnon solution in one subspace we show that its dispersion relation is associated with that of ..."
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In the string theory in AdS4 × CP 3 we construct the giant magnon and spike solutions with two spins in two kinds of subspaces of Rt×CP 3 and derive the dispersion relations for them. For the single giant magnon solution in one subspace we show that its dispersion relation is associated with that of the big onespin giant magnon solution in the RP 2 subspace. For the single giant magnon solution in the other complementary subspace its dispersion relation is similar to that of the onespin giant magnon solution living in the S 2 subspace but has one additional spin dependence.
Giant magnons on CP 3 by dressing method
"... We consider classical string spectrum of Rt × CP 3, and construct a family of solutions with residual SU(2) symmetry by the dressing method on SU(4)/U(3) sigma model. All of them obey the squareroot type dispersion relation often found in the theory with su(22) symmetry. A single dyonic giant magn ..."
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We consider classical string spectrum of Rt × CP 3, and construct a family of solutions with residual SU(2) symmetry by the dressing method on SU(4)/U(3) sigma model. All of them obey the squareroot type dispersion relation often found in the theory with su(22) symmetry. A single dyonic giant magnon is not found in this approach.
FiniteSize Corrections of the CP 3 Giant Magnons: the Lüscher terms,” [arXiv:0810.0704
 in the SU(2) × SU(2) sector of AdS4 × CP 3 ,” [arXiv:0810.1246
"... We compute classical and first quantum finitesize corrections to the recently found giant magnon solutions in two different subspaces of CP 3. We use the Lüscher approach on the recently proposed exact Smatrix for N = 6 superconformal ChernSimons theory. We compare our results with the string and ..."
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We compute classical and first quantum finitesize corrections to the recently found giant magnon solutions in two different subspaces of CP 3. We use the Lüscher approach on the recently proposed exact Smatrix for N = 6 superconformal ChernSimons theory. We compare our results with the string and algebraic curve computations and find agreement, thus providing a nontrivial test for the new AdS4/CFT3 correspondence within an integrability framework. 1
Finitesize Effect of the Dyonic Giant Magnons in N = 6 super ChernSimons Theory
, 810
"... We consider finitesize effects for the dyonic giant magnon of the type IIA string theory on AdS4 × CP 3 by applying Lüscher µterm formula which is derived from a recently proposed Smatrix for the N = 6 super ChernSimons theory. We compute explicitly the effect for the case of a symmetric configu ..."
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We consider finitesize effects for the dyonic giant magnon of the type IIA string theory on AdS4 × CP 3 by applying Lüscher µterm formula which is derived from a recently proposed Smatrix for the N = 6 super ChernSimons theory. We compute explicitly the effect for the case of a symmetric configuration where the two external bound states, each of A and B particles, have the same momentum p and spin J2. We compare this with the classical string theory result which we computed by reducing it to the NeumannRosochatius system. The two results match perfectly. On leave from Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,
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
arXiv:1111.2839v3 Real and Virtual Bound States in Lüscher Corrections for CP 3 Magnons
, 2011
"... We study classical and quantum finitesize corrections to giant magnons in AdS4 × CP 3 using generalised Lüscher formulae. Lüscher Fterms are organised in powers of the exponential suppression factor (e−∆/2h)m, and we calculate all terms in this series, matching oneloop algebraic curve results ..."
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We study classical and quantum finitesize corrections to giant magnons in AdS4 × CP 3 using generalised Lüscher formulae. Lüscher Fterms are organised in powers of the exponential suppression factor (e−∆/2h)m, and we calculate all terms in this series, matching oneloop algebraic curve results from our previous paper [1]. Starting with the second term, the structure of these terms is different to those in AdS5 × S5 thanks to the appearance of heavy modes in the loop, which can here be interpreted as twoparticle bound states in the mirror theory. By contrast, physical bound states can represent dyonic giant magnons, and we also calculate Fterms for these solutions. Lüscher µterms, suppressed by e−∆/E, instead give at leading order the classical finitesize correction. For the elementary dyonic giant magnon we recover the correction given by [2]. We then extend this to calculate the next term in 1/h, giving a oneloop prediction. Finally we also calculate Fterms for the various composite giant magnons, RP 3 and ‘big’, again finding agreement to all orders.
Strings in AdS4 × CP 3: finite size spectrum vs.
"... Abstract:We compute the first curvature corrections to the spectrum of lightcone gauge type IIA string theory that arise in the expansion of AdS4×CP 3 about a planewave limit. The resulting spectrum is shown to match precisely, both in magnitude and degeneration that of the corresponding solutions ..."
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Abstract:We compute the first curvature corrections to the spectrum of lightcone gauge type IIA string theory that arise in the expansion of AdS4×CP 3 about a planewave limit. The resulting spectrum is shown to match precisely, both in magnitude and degeneration that of the corresponding solutions of the allloop Gromov–Vieira Bethe Ansatz. The oneloop dispersion relation correction is calculated for all the single oscillator states of the theory, with the level matching condition lifted. It is shown to have all logarithmic divergences cancelled and to leave only a finite exponentially suppressed contribution, as shown earlier for light bosons. We argue that there is no ambiguity in the choice of the regularization for the selfenergy sum, since the regularization applied is the only one preserving unitarity. Interaction matrices in the full degenerate twooscillator sector are calculated and the spectrum of all two light magnon oscillators is completely determined. The same finitesize corrections, at the order 1J, where J is the length of the chain, in the twomagnon sector are calculated from the all loop Bethe Ansatz. The corrections obtained by the two completely different methods coincide up to the fourth order in λ ′ ≡ λ J2. We conjecture that the equivalence extends to all orders in λ ′ and to higher orders in 1J.
M2brane Perspective on N = 6 Super ChernSimons Theory at Level k
, 810
"... Recently, O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena (ABJM) proposed threedimensional super ChernSimonsmatter theory, which at level k is supposed to describe the low energy limit of N M2branes. For large N and k, but fixed ’t Hooft coupling λ = N/k, it is dual to type IIA string th ..."
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Recently, O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena (ABJM) proposed threedimensional super ChernSimonsmatter theory, which at level k is supposed to describe the low energy limit of N M2branes. For large N and k, but fixed ’t Hooft coupling λ = N/k, it is dual to type IIA string theory on AdS4 × CP 3. For large N but finite k, it is dual to M theory on AdS4 × S 7 /Zk. In this paper, relying on the second duality, we find exact giant magnon and single spike solutions of membrane configurations on AdS4 × S 7 /Zk. We derive the dispersion relations and their finitesize corrections with explicit dependence on the level k, by reducing the system to the NeumannRosochatius integrable model. On leave from Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,
J H E P11(2008)069 Published by IOP Publishing for SISSA
, 2008
"... Quantum spinning strings in AdS4 × CP 3: testing the ..."
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Generalized Dynamical Spin Chain and 4Loop Integrability in
, 904
"... We revisit unitary representation of centrally extended psu(22) excitation superalgebra. We find most generally that ‘pseudomomentum’, not lattice momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic spin chain. All known results point to lattice momentum diagonalization ..."
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We revisit unitary representation of centrally extended psu(22) excitation superalgebra. We find most generally that ‘pseudomomentum’, not lattice momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic spin chain. All known results point to lattice momentum diagonalization forN = 4 super YangMills theory. Having different interacting structure, we ask ifN = 6 superconformal ChernSimons theory provides an example of pseudomomentum diagonalization. For SO(6) sector, we study maximal shuffling and nexttomaximal shuffling terms in the dilatation operator and compare them with results expected from psu(22) superalgebbra and integrability. At two loops, we rederive maximal shuffling term (3site) and find perfect agreement with known results. At four loops, we first find absence of nexttomaximal shuffling term (4site), in agreement with prediction based on integrability. We next extract maximal shuffling term (5site), the most relevant term for checking the possibility of pseudomomentum diagonalization. Curiously, we find that result agrees with integraility prediction based on lattice momentum, as inN = 4 super YangMills theory. Consistency of our