Abstract
We study finite-size corrections to the magnon dispersion relation in three models which differ from string theory on AdS5 × S5 in their boundary conditions. Asymptotically, this is accomplished by twisting the transfer matrix in a way which manifestly preserves integrability. In model I all world-sheet fields are periodic, whereas model II represents a particular orbifold of AdS5 × S5 and model III is a β-deformed theory. For models I and II we construct the one-particle TBA equations and use them to determine the leading finite-size correction to the asymptotic Bethe equation. We also make some interesting observations concerning the quantization conditions for the momentum. For the same models we compute the leading and for model II the next-to-leading order finite-size corrections to the asymptotic magnon dispersion relation. Furthermore, we apply Lüscher’s formulae to compute the leading finite-size corrections in β-deformed theory. In addition to reproducing known results, we provide new predictions for two-particle states from the \( \mathfrak{s}\mathfrak{l}(2) \) sector, to be confronted with explicit field-theoretic calculations in the dual gauge theory. Finally, we prove that the leading finite-size correction to the energy of an \( \mathfrak{s}\mathfrak{l}(2) \) magnon in orbifold theory is the same as the one for an \( \mathfrak{s}\mathfrak{u}(2) \) magnon in β-deformed theory for special values of β. We also speculate that for these values of β our result for the next-to-leading order correction in the orbifold model might coincide with the corresponding correction to the energy of an \( \mathfrak{s}\mathfrak{u}(2) \) magnon in β-deformed theory.
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ArXiv ePrint: 1009.4118
Correspondent fellow at Steklov Mathematical Institute, Moscow. (Gleb Arutyunov)
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Arutyunov, G., de Leeuw, M. & van Tongeren, S.J. Twisting the mirror TBA. J. High Energ. Phys. 2011, 25 (2011). https://doi.org/10.1007/JHEP02(2011)025
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DOI: https://doi.org/10.1007/JHEP02(2011)025