Vector-like models with O(N) and U(N) symmetries at their critical points were seen to exhibit duality with higher spin gravitational theories of Vasiliev. In the dissertation, we study the finite temperature Vector Model/Higher Spin Duality in Large N. For CFTs given by 3d O(N) (or U(N)) vector models, I evaluate the leading and one-loop partition functions in a variety of geometries. This calculations are performed in the scheme of collective field theory, which was seen in earlier studies to represent a bulk description of Vasiliev higher spin theory. The calculations presented provide data for comparison of small fluctuation determinants, giving further evidence for the one-to-one bulk identification between the bi-local and the AdS picture. They also o er insight into the identification of coupling constants G and 1/N of the two descriptions for models based on O(N) symmetry. I also consider the canonical structure of the collective formulation of Vector Model/Higher Spin Duality in AdS4. This formulation involves a construction of bulk AdS Higher Spin fields through a time-like bi-local Map, with a Hamiltonian and canonical structure that are established to all orders in 1/N. Finally, I study the Large N dynamics of the O(N) field theory in the Thermo field dynamics approach. The question of recovering the high temperature phase and the corresponding O(N) gauging is clarified. Through the associated bi-local representation, we discuss the emergent bulk space-time and construction of (Higher spin) fields. We note the presence of “evanescent” modes in this construction and also the mixing of spins at finite temperature.
Yoon, Junggi,
"Finite Temperature Holography in Higher Spin Theory/Vector Model"
(2016).
Physics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0TB15BW
