| 1. |
- Beisert, Niklas, et al.
(author)
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Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
- 2005
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In: Nuclear Physics B. - : Elsevier BV. - 0550-3213. ; 715, s. 190-210
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Journal article (peer-reviewed)abstract
- We compare quantum corrections to semiclassical spinning strings in AdS(5)xS(5) to one-loop anomalous dimensions in N=4 supersymmetric gauge theory. The latter are computed using the reduced (Landau-Lifshitz) sigma model and with the help of the Bethe ansatz. The results of all three approaches are in remarkable agreement with each other. As a byproduct we establish the relationship between linear instabilities in the Landau-Lifshitz model and analyticity properties of the Bethe ansatz.
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| 2. |
- Minahan, Joseph A., et al.
(author)
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1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
- 2006
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In: Nuclear Physics B. ; 735, s. 127-171
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Journal article (peer-reviewed)abstract
- 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 with the string theory world-sheet action up to the first two orders in the effective parameter $\tilde{\lambda} ={\lambda / J^2}$, where $\lambda$ 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 $\beta$-deformed LL action and find that the quantum LL result is again equal to the 1/J correction computed from the $\beta$-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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