Classical/quantum integrability in non-compact sector of AdS/CFT

V. A. Kazakov (1) , K. Zarembo

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

We discuss non-compact SL(2,R) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of the classical sigma model and show that at one loop it is identical to the classical limit of Bethe equations of the spin (-1/2) chain for the dilatation operator of SYM.

Domaines: Systèmes Solubles et Intégrables [nlin.SI]; Physique des Hautes Energies - Théorie [hep-th]

V. A. Kazakov, K. Zarembo. Classical/quantum integrability in non-compact sector of AdS/CFT. Journal of High Energy Physics, 2004, 0410, pp.60. ⟨hal-00256757⟩