# Princeton University Library Catalog

- Author/Artist:
- Tan, Zhong Ming [Browse]
- Format:
- Senior thesis
- Language:
- English
- Advisor(s):
- Giombi, Simone [Browse]
- Contributor(s):
- Klebanov, Igor [Browse]
- Department:
- Princeton University. Department of Physics [Browse]
- Class year:
- 2014
- Description:
- 110 pages
- Summary note:
- In this senior thesis, we explore two aspects of Vasiliev higher-spin theory, a theory of gravity that
can be defined consistently for non-zero cosmological constant and contains massless particles
with spin greater than 2 in its spectrum. Much interest pertaining to this field is due to the
establishment of a gravity/gauge duality conjecture by Klebanov and Polyakov between Vasiliev
theory in AdSd+1 space and the O(N) vector model in conformal field theory (CFT) of dimension d.
In the first part, we study the theory in terms of its equations of motion. While equations of motion
have been derived for Vasiliev theory, much remains to be explored about them, with only a handful
of solutions to these equations of motion been discovered. Here, we study and constrain possible
solutions to the Vasiliev equations of motion involving only spin-0, 1 and 2 fields, even though
generically solutions to Vasiliev equations of motion involve an infinite tower of higher-spin fields.
In the second part, we study the theory by testing the gravity/gauge duality conjecture between
Vasiliev theory and the generalization of the O(N) model that includes both scalar and fermonic
fields in the fundamental representation of O(N). We compute one-loop free energy contributions of
half-integer higher spins on the AdSd+1 side and match them to the O(N0) correction to the Sd free
energy on the CFT side, which is expected to be trivial. This requires evaluating a regularized sum
over one loop vacuum energies of an infinite set of massless half-integer higher spin gauge fields
in Euclidean AdSd+1. We show that the one-loop free energies on both ends vanish identically,
thereby providing further non-trivial evidence for the conjecture. We also compute changes to the
free-energy due to the imposition of different boundary conditions on the bulk higher spin fields,
which are expected to induce conformal higher spin theories at the boundary.