Bahaa Elshimy Qualifying Exam

Abstract: There is significant motivation to study 2D Toda theory, whether as one side of the AGT correspondence, or as the boundary theory of some 3D semiclassical bulk theory whose asymptotic symmetry is given by two copies of the Wn algebra (i.e. a higher-spin generalization of Brown-Henneaux), or simply as the generalization of Liouville Theory.  In this talk, I will motivate the study of Toda theory from these perspectives and introduce a framework for analyzing its correlation functions using the Probabilistic Method. This approach leads to new constraints on the theory’s parameter space, including bounds on the coupling constant and the momenta. The equivalent of the Seiberg bound will be discussed and parameter space subregions of singular and vanishing moments and cross-moment will be highlighted. Time-permitting I will also outline progress made towards the 3D bulk dual given this approach.