Twisting the Mirror TBA

TL;DR

This paper investigates finite-size effects on magnon dispersion in three integrable models related to AdS/CFT, deriving corrections using TBA and Lüscher's formulas, and providing new predictions for dual gauge theories.

Contribution

It introduces a unified approach to compute finite-size corrections in twisted integrable models, including new predictions for two-particle states in the dual gauge theory.

Findings

Derived one-particle TBA equations for models I and II

Computed leading and next-to-leading finite-size corrections to magnon dispersion

Predicted new finite-size correction results for two-particle states in the sl(2) sector

Abstract

We study finite-size corrections to the magnon dispersion relation in three models which differ from string theory on AdS5 x 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 x S5 and model III is a beta-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 L\"uscher's formulae to compute the leading finite-size corrections in beta-deformed theory. In addition to reproducing known results, we provide new predictions for two-particle states from the sl(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 sl(2) magnon in orbifold theory is the same as the one for an su(2) magnon in beta-deformed theory for special values of beta. We also speculate that for these values of beta our result for the next-to-leading order correction in the orbifold model might coincide with the corresponding correction to the energy of su(2) magnon in beta-deformed theory.