image corrections to semiclassical AdS/CFT states from quantum Landau–Lifshitz model Original Research Article

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 parameter image, where λ is the ʹt Hooft coupling and J is the total R-charge. Here we address the question if quantizing the effective LL action reproduces the subleading image 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 image corrections to energies of BMN states as found previously on the gauge theory and string theory sides. We also compute the subleading image 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 image 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 image corrections to the classical energies. We emphasize the simplicity of this effective field theory approach as compared to the full quantum string computations.