Spin Chains and String Theory

Kruczenski, Martín

doi:10.1103/physrevlett.93.161602

Cited by 296 publications

(667 citation statements)

References 42 publications

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“…A very simple and clear way of establishing the correspondence between "fast" strings and low-energy "coherent" spin chain states representing dual gauge-theory operators was suggested in [14] and further clarified and developed in [15,16,17] (for a review see [10]; various extensions were considered in [18,19,20,21,22,23,24]). …”

Section: Introductionmentioning

confidence: 99%

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corrections to semiclassical AdS/CFT states from quantum Landau–Lifshitz model

Minahan

Tirziu²,

Tseytlin³

2006

Nuclear Physics B

151

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One way to relate semiclassical string states and dual gauge theory states is to show the equivalence between their low-energy effective 2d actions. The gauge theory effective action, which is represented by an effective Landau-Lifshitz (LL) model, was previously found to match the string theory world-sheet action up to the first two orders in the effective parameterλ = λ/J 2 , where λ is the 't Hooft coupling and J is the total R-charge. Here we address the question if quantizing the effective LL action reproduces the subleading 1/J corrections to the spin chain energies as well as the quantum corrections to the string energies. We demonstrate that this is indeed the case provided one chooses an appropriate regularization of the effective LL theory. Expanding near the BPS vacuum, we show that the quantum LL action gives the same 1/J corrections to energies of BMN states as found previously on the gauge theory and string theory sides. We also compute the subleading 1/J 2 corrections and show that these too match with corrections computed from the Bethe ansatz. We also compare the results from the LL action with a more direct computation from the spin chain. We repeat the same computation for the β-deformed LL action and find that the quantum LL result is again equal to the 1/J correction computed from the β-deformed Bethe ansatz equations. We also quantize the LL action near the rotating circular and folded string solutions, generalizing the known gauge/string results for 1/J corrections to the classical energies. We emphasize the simplicity of this effective field theory approach as compared to the full quantum string computations.

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Section: Introductionmentioning

confidence: 99%

“…2 Landau-Lifshitz action in the SU (2) sector Let us start with recalling the derivation of the effective Landau-Lifshitz action on both the gauge theory (spin chain) and the string theory sides [14,15,10].…”

Section: Introductionmentioning

confidence: 99%

corrections to semiclassical AdS/CFT states from quantum Landau–Lifshitz model

Minahan

Tirziu²,

Tseytlin³

2006

Nuclear Physics B

151

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“…Instead we should take the 2d T-dual along ζ(σ) and introduce the T-dualized field ζ(σ), then gauge-fix as ζ(σ) = Jσ/ √ λ just as was done in [34]. For more details, see [27,28,34].…”

Section: Large-spin Limit Of Spinning Strings Onmentioning

confidence: 99%

“…Following [27,34,43], let us perform a so-called "coherent state path integral" to obtain an effective action. First we consider the path integral for one spin, i.e., for one site in the chain.…”

Section: Brief Review On Deformed Theories and Coherent State Action mentioning

confidence: 99%

“…To emphasize more on the correspondence between the spin-chain and spinning string in the deformed cases, we first adopt a different approach from [38], instead we will use the LandauLifshitz sigma model approach as in [27,28], and show the equivalence between the coherent state action of twisted spin chain and the fast-string limit of sigma model action in Lunin-Maldacena background. This part overlaps with the materials presented in [34], however we decide to keep it for completeness as well as being a good entry route for establishing the correspondence.…”

Section: Introductionmentioning

confidence: 99%

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The anatomy of gauge/string duality in Lunin-Maldacena background

Chen

Okamura

2006

J. High Energy Phys.

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We consider the correspondence between the spinning string solutions in Lunin-Maldacena background and the single trace operators in the Leigh-Strassler deformation of N = 4 SYM. By imposing an appropriate rotating string ansätz on the Landau-Lifshitz reduced sigma model in the deformed SU (2) sector, we find two types of 'elliptic' solutions with two spins, which turn out to be the solutions associated with the Neumann-Rosochatius system. We then calculate the string energies as functions of spins, and obtain their explicit forms in terms of a set of moduli parameters.On the deformed spin-chain side, we explicitly compute the one-loop anomalous dimensions of the gauge theory operators dual to each of the two types of spinning string solutions, extending and complementing the results of hep-th/0511164. Moreover, we propose explicit ansätz on how the locations of the Bethe strings are affected due to the deformation, with several supports from the string side.

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The SU(2) sector in AdS/CFT

Minahan

2005

Fortschritte der Physik

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In the large N limit of N = 4 Super Yang-Mills, the mixing under dilatations of the SU(2) sector, single trace operators composed of L complex scalar fields of two types, is closed to all orders in perturbation theory. By relying on the AdS/CFT correspondence, and by examining the currents for semiclassical strings, we present evidence which implies that there are small mixings that contradict the closure of the SU(2) sector in the strong coupling limit. These mixings first appear to second order in the λ/L 2 expansion.To appear in proceedings of the RTN workshop, "The quantum structure of space-time and the geometric nature of fundamental interactions", Kolymbari, Crete, September 2004.

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Spin Chains and String Theory

Cited by 296 publications

References 42 publications

corrections to semiclassical AdS/CFT states from quantum Landau–Lifshitz model

corrections to semiclassical AdS/CFT states from quantum Landau–Lifshitz model

The anatomy of gauge/string duality in Lunin-Maldacena background

The SU(2) sector in AdS/CFT

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