Interactions of conformal and partially massless higher spin fields

Abstract

This thesis investigates the interactions of partially massless (PM) fields in 4-dimensional (anti)de Sitter spaces, along with conformal higher spin fields and their coupling to matter in arbitrary dimensions. The first part of the thesis deals with PM fields and PM algebras. A reformulation of PM fields is proposed and studied using a novel chiral formulation, inspired by Penrose's twistor approach to massless fields in Minkowski space. This reformulation enables explicit construction of Yang-Mills-type interactions and current couplings. Next, an oscillator realisation for PM higher spin algebras is given in terms of bosonic and fermionic oscillators. The construction is based on the Weyl-Clifford algebra. The second part of the thesis derives the coupling between a massless scalar field and a background of higher spin fields within a manifestly covariant framework, employing Fedosov quantization techniques, called the "parent formulation". This formalism yields, in particular, an explicit covariant expression for the coupling between scalar fields and higher spin conformal gravity.

Figures (4)

• Figure 1: A diagram to show fields/coordinates involved into the description of partially massless higher spin fields. Along the horizontal/vertical axe, we have the number of unprimed/primed indices on a spin-tensor. Components of the $1$-form connection are represented by green circles, while the $0$-forms (the Weyl tensor and its descendants) are represented by red rectangles. By descendants we mean the on-shell nontrivial derivatives of the Weyl tensor, which are associated with the coordinates on the on-shell jet space Penrose:1986ca.
• Figure 2: For a given spin-$s$, the fields grouped horizontally/vertically correspond to chiral/anti-chiral description of depth-$t$ partially massless fields. There are two descriptions for each admissible $s$, and $t$. The group on each of the axes describes massless fields in terms of (anti-)chiral variables. It is clear that extrapolation of one description beyond $t>s$ does give the other one.
• Figure 3: In blue, the region covered by descendants of $\Psi^{A(s-k+1),A'(s+k-1)}$, in red the descendants of $\Psi^{A(s+k-1),A'(s-k+1)}$ and in gray the overlap between these two regions.
• Figure :

Theorems & Definitions (2)

• Definition A.1
• Definition C.1