Large spin limit of AdS5×S5 string theory and low energy expansion of ferromagnetic spin chains
By M. Kruczenski, A. Ryzhov, A. Tseytlin. 2004
259 citations recorded by the source corpus.
Abstract By considering AdS 5 × S 5 string states with large S 5 angular momenta one can provide non-trivial quantitative checks of the AdS/CFT duality. A string rotating in S 5 with two angular momenta J 1 , J 2 is dual to an operator in N =4 SYM theory whose conformal dimension can be computed by diagonalizing a (generalization of) spin 1/2 Heisenberg chain Hamiltonian. It was recently argued and verified to lowest order in a large J = J 1 + J 2 expansion, that the Heisenberg chain can be described using a non-relativistic low energy effective 2d action for a unit vector field n i which exactly matches the corresponding large J limit of the classical AdS 5 × S 5 string action. In this paper we show that this agreement extends to the next order and develop a systematic procedure for computing higher orders in such large angular momentum expansion. This involves several non-trivial steps. On the string side, we need to choose a special gauge with a non-diagonal world-sheet metric which insures that the angular momentum is uniformly distributed along the string, as indeed is the case on the spin chain side. We need also to implement an order by order redefinition of the field n i to get an action linear in the time derivative. On the spin chain side, it turns out to be crucial to include the effects of integrating out short wave-length modes. In this way we gain a better understanding of how (a subsector of) the string sigma model emerges from the dual gauge theory, allowing us to demonstrate the duality beyond comparing particular examples of states with large J .
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/84380247e02c1800e4f138cdc133922e1959fa01
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Citations in the corpus
- Finite-size effects from giant magnons (2006, methodology): “These gauges generalize the standard phase-space light-cone gauge of [44] to a curved background, and have been used to study the dynamics of strings in AdS5 × S5 [20,25,45–49].”
- Spinning strings in AdS5 × S5: one-loop correction to energy in SL(2) sector (2005, methodology): “Here using a non-conformal “homogeneous” gauge similar to the one used in the SU(2) case [ 31 , 35] we will show how to compute subleading terms in the expansion of the string action for a general (S, J) closed string configuration with a non-zero winding m along a big circle in S5 (ref.[33] conside”
- Classical/quantum integrability in AdS/CFT (2004, background): “We later received [83], where it was shown that the effective action for the Heisenberg chain can be mapped onto the string action to at least two-loop order.”
- Gauge-string duality for (non)supersymmetric deformations of N=4 super-Yang–Mills theory (2005, methodology): “As in [2], they can be systematically described by reducing the classical string action to a kind of “Landau-Lifshitz” (LL) sigma model [12, 13] for the “transverse” string degrees of freedom.”
- Pulsating strings on Ads(5) x S(5) (2004, background): “ help in providing a bridge between duality checks at the level of individual solutions and higher-level checks. An example of the latter is the recent analysis of the duality at the level of actions [68, 69, 70, 71, 72, 73]. We will analyse the case at hand from the gauge side and string side in se”
- The off-shell symmetry algebra of the light-cone AdS5 × S5 superstring (2006, background): “A suitable gauge which leads to the removal of non-physical degrees of freedom has been introduced in [20], following earlier work in [7, 8, 10, 23, 24].”
- INTEGRABILITY IN QCD AND BEYOND (2004, background): “ One can improve the effective sigma model action (6.15) by calculating corrections involving higher derivatives of the fields. All such terms containing up to four derivatives have been found in Refs. [129,130]. 6.2. Semiclassical string motion and integrable models We have argued above that the effec”
- On one-loop correction to energy of spinning strings in S**5 (2004, background): “Related aspect of this problem is that the spin chain states found using the Bethe ansatz [10] are exact quantum states, while on the string theory side we are considering semiclassical states dual to coherent states of the spin chain [19, 21 , 30].”
- Spiky strings and giant magnons on S5 (2006, unknown): “The semi-classical nature of these states was emphasized in [8, 9] where also a direct relation between the two low-energy effective field theory systems was described.”
- The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations (2006, background): “This Hamiltonian can be considered as an effective Hamiltonian for the su(2) sector, and its expansion in powers of λ′ should reproduce the Landau–Lifschitz Hamiltonian derived in [39, 47].”