Studies in Vasiliev Higher Spin Theory

Abstract

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.