Date: 
July 16, 2008
 10:30  12:00
 13:30  15:00
 15:30  17:00

Place: 
Seminar Room at IPMU Prefab. B, Kashiwa Campus of the University of Tokyo 
Speaker: 
Kazuhiro Sakai (Keio) 
Title: 
AdS/CFT correspondence and Integrable systems

Abstract: 
Integrability has become of increasing importance in the study of the
AdS/CFT correspondence, the duality between the fourdimensional
maximally supersymmetric gauge theory and the IIB superstring theory
over the AdS_{5} x S^{5} background. Integrable structures were found
independently on both sides of the correspondence, first at oneloop
order of perturbation on the gauge side and in the classical limit
on the string side. These structures were subsequently unified into
a novel integrable structure which is valid for arbitrary values
of the coupling. I will explain how these structures emerge from the
original theories and how they help us to solve the spectral problems
in the AdS/CFT correspondence. The plan of the lecture is as follows:
 1) Classical superstrings: finitegap solutions and spectral curves
 2) Gauge theory at oneloop: integrable spinchain and Bethe ansatz
 3) Allorder integrability: particle model and su(22) factorized Smatrix
