Wronskian solution for AdS/CFT Y-system

Nikolay Gromov (1) , Vladimir Kazakov (2, 3) , Sebastien Leurent (2) , Zengo Tsuboi (4, 5)

1 St. Petersburg Nuclear Physics Institute
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
3 UPMC - Université Pierre et Marie Curie - Paris 6
4 OCAMI - Osaka City university Advanced Mathematical Institute [Osaka]
5 Institute for Quantum Physics

Using the discrete Hirota integrability we find the general solution of the full quantum Y-system for the spectrum of anomalous dimensions of operators in the planar AdS5/CFT4 correspondence in terms of Wronskian-like determinants parameterized by a finite number of Baxter's Q-functions. We consider it as a useful step towards the construction of a finite system of non-linear integral equations (FiNLIE) for the full spectrum. The explicit asymptotic form of all the Q-functions for the large size operators is presented. We establish the symmetries and the analyticity properties of the asymptotic Q-functions and discuss their possible generalization to any finite size operators.

Mots clés: AdS-CFT Correspondence; Integrable Field Theories

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Nikolay Gromov, Vladimir Kazakov, Sebastien Leurent, Zengo Tsuboi. Wronskian solution for AdS/CFT Y-system. Journal of High Energy Physics, 2011, 01, pp.155. ⟨10.1007/JHEP01(2011)155⟩. ⟨hal-00716820⟩