This dissertation summarizes studies directed at a deeper understanding of the AdS/CFT correspondence, its origin and its dynamics. First, classical strings in AdS were considered and a general method for constructing string solutions was developed. The method is based on the reduction of string sigma models to integrable equations of sinh-Gordon or more generally Toda type. These equations are characterized by soliton type solutions from which the string configurations are constructed with a one-to-one correspondence between solitons of the field theory and spikes of the string. Through this correspondence the most general class of dynamical string solutions can be generated. In the case of AdS3, these general spiky strings are characterized by an arbitrary number n of spikes and two arbitrary holomorphic functions. After fixing the conformal frame, only the soliton moduli remain, giving a specification of the string moduli. This moduli space is particle-like and it is shown that the spikes follow a closed set of equations describing the dynamics of the moduli space providing a 0-brane picture of the AdS string.In the second part of the dissertation we pursue the direct construction of the AdS theory from the large N collective dynamics of its moduli. We accomplish this fully in the simplest sub-sector corresponding to the bi-local system of n=2 spikes. It is seen that higher spin massless particles originate from the cusps of the spiky strings. The large N collective construction establishes the proposal of Klebanov and Polyakov that higher-spin AdS gravity of Vasiliev's type appears as a dual to the O(N) vector model. For this an explicit mapping of the AdS4 spacetime (and of higher-spin fields) was given from collective (bi-local) fields. This construction was deduced through the identification of isometries of SO(2,3) with the conformal generators of the CFT3 in the light-cone quantization. This mapping gives an explicit derivation of the extra spatial dimension in the AdS spacetime and reconstruction of the bulk AdS theory.
Jin, Kewang,
"String Dynamics and Higher Spin Anti-de Sitter Gravity"
(2011).
Physics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0MW2FD4
