Investigation of higher spin theory through holography and mathematical methods in free conformal field theory
In this dissertation, we will develop novel methods for determining the spectrum of primary operators in a free conformal eld theory (vector model) and to construct some of these primaries. To count the spectrum of primaries, we use group theoretic techniques to obtain character formulas for any number of elds as representations of SO(4; 2). More precisely, we will construct generating functions that can be expanded to any order in the conformal scaling dimension to yield the complete spectrum of primaries constructed out of n scalar elds. We also develop e cient methods to construct these primaries by using a polynomial description. Finally, these primary operators, which are higher spin currents in the free conformal vector model, correspond to higher spin gauge elds in Vasiliev higher spin theory through the holographic duality.
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science. January 2017.
Rabe, Randle (2017) Investigation of higher spin theory through holography and mathematical methods in free conformal field theory, , University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/23459>