Neumann-Rosochatius integrable system for strings onAdS4× ℂℙ3

We analyze several aspects of the recent construction of three-dimensional conformal gauge theories by Aharony et al. in various regimes. We pay special attention to understanding how the M-theory geometry and interpretation can be extracted from the analysis of the field theory. We revisit the calculations of the moduli space of vacua and the complete characterization of chiral ring operators by analyzing the field theory compactified on a 2-sphere. We show that many of the states dual to these operators can be interpreted as D-brane states in the weak coupling limit.Also, various features of the dual AdS geometry can be obtained by performing a strong coupling expansion around moduli space configurations, even though one is not taking the planar expansion. In particular, we show that at strong coupling the corresponding weak coupling D-brane states of the chiral ring localize on particular submanifolds of the dual geometry that match the M-theory interpretation. We also study the massive spectrum of fields in the moduli space. We use this to investigate the dispersion relation of giant magnons from the field theory point of view. Our analysis predicts the exact functional form of the dispersion relation as a function of the world-sheet momentum, independently of integrability assumptions, but not the exact form with respect to the 't Hooft coupling. We also get the dispersion relation of bound states of giant magnons from first principles, providing evidence for the full integrability of the corresponding spin chain model at strong 't Hooft coupling.

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“…This bound state relation is similar to the one found by Dorey [89]. Giant magnon solutions of the string sigma model also show this result [90].…”

Section: Dispersion Relation Of the Giant Magnonsupporting

confidence: 88%

Three-dimensionalN=6superconformal field theories and their membrane dynamics

2008

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“…It is only natural to choose the gauge 25) which eliminates from the fermion fields the components not appearing in the Lagrangian. This algebraic gauge, which is similar to the light-cone gauge, introduces no κ-symmetry ghosts.…”

Section: Jhep12(2008)101mentioning

confidence: 99%

Spinning strings at one-loop in AdS₄× ℙ³

McLoughlin¹,

Roiban²

2008

J. High Energy Phys.

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Abstract:We analyze the folded spinning string in AdS 4 × P 3 with spin S in AdS 4 and angular momentum J in P 3 . We calculate the one-loop correction to its energy in the scaling limit of both ln S and J large with their ratio kept fixed. This result should correspond to the first subleading strong coupling correction to the anomalous dimension of operators of the type T r(D S (Y † Y ) J ) in the dual N = 6 Chern-Simons-matter theory. Our result appears to depart from the predictions for the generalized scaling function found from the all-loop Bethe equations conjectured for this AdS 4 /CFT 3 duality. We comment on the possible origin of this difference.

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“…Further, the giant magnon and spike solutions with two angular momenta have been constructed by reducing the string dynamics on AdS 4 × CP 3 to the Neumann-Rosochatius integrable system [16], where the dispersion relations and the finite-size corrections for them have been computed. On the other hand from the analysis of the finite gap algebraic curve the dispersion relation of the giant magnon and the one-loop quantum correction have been presented [17].…”

Section: Jhep11(2008)084mentioning

confidence: 99%

“…[16] the four embedding complex coordinates constrained by a CP 3 condition have been used for parametrizing the CP 3 space to construct the string moving in R t ×S 3 × S 3 with two angular momenta in the first S 3 and with exactly opposite angular momenta in the second S 3 , and extract the dispersion relation of a single giant magnon solution living in S 3 with two angular momenta. We will choose the spherical coordinates of CP 3 space presented in ref.…”

Section: Jhep11(2008)084mentioning

confidence: 99%

Giant magnon and spike solutions with two spins inAdS₄×CP³

Ryang¹

2008

J. High Energy Phys.

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In the string theory in AdS 4 × CP 3 we construct the giant magnon and spike solutions with two spins in two kinds of subspaces of R t × 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 one-spin 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 one-spin giant magnon solution living in the S 2 subspace but has one additional spin dependence.

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Neumann-Rosochatius integrable system for strings onAdS₄× ℂℙ³

Cited by 46 publications

References 33 publications

Three-dimensionalN=6superconformal field theories and their membrane dynamics

Three-dimensionalN=6superconformal field theories and their membrane dynamics

Spinning strings at one-loop in AdS₄× ℙ³

Giant magnon and spike solutions with two spins inAdS₄×CP³

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Neumann-Rosochatius integrable system for strings onAdS4× ℂℙ3

Cited by 46 publications

References 33 publications

Three-dimensionalN=6superconformal field theories and their membrane dynamics

Three-dimensionalN=6superconformal field theories and their membrane dynamics

Spinning strings at one-loop in AdS4× ℙ3

Giant magnon and spike solutions with two spins inAdS4×CP3

Contact Info

Product

Resources

About

Neumann-Rosochatius integrable system for strings onAdS₄× ℂℙ³

Spinning strings at one-loop in AdS₄× ℙ³

Giant magnon and spike solutions with two spins inAdS₄×CP³