Algebraic curves for integrable string backgrounds

Many Ramond–Ramond backgrounds that arise in the AdS/CFT correspondence are described by integrable sigma-models. The equations of motion for classical spinning strings in these backgrounds can be solved quite generally by the finite-gap integration method via classical Bethe equations and algebraic curves. This construction is reviewed for general $\mathbb Z_4$ cosets and then exemplified by the backgrounds that arise in the AdS$_5$/CFT$_4$, AdS$_4$/CFT$_3$ and AdS$_3$/CFT$_2$ dualities.

Поступило в апреле 2010 г.