Formulation of Free Higher Spin Supersymmetric Theories in Superspace

TL;DR

This thesis formulates free higher spin superfield theories in four-dimensional superspace, exploring their geometrical structure, superspin classifications, and connections to five-dimensional theories, including new insights into superspace Casimir operators.

Contribution

It provides the first superfield actions for massive higher spin multiplets and introduces the super projector method to analyze superspace geometries and their relation to higher-dimensional theories.

Findings

Superfield actions for massless and massive higher spin supermultiplets are constructed.

The super projector method clarifies the geometrical structure of superspace actions.

New superspace Casimir operators for anti-de Sitter backgrounds are derived.

Abstract

The N = 1 superfield formalism in four-dimensions is well formulated and understood, yet there remain unsolved problems. In this thesis, superfield actions for free massless and massive higher spin superfield theories are formulated in four dimensions. The discussion of massless models is restricted to half integer superhelicity. These models describe multiplets with helicities (s, s-1/2) where s is an integer. The investigation of massive models covers recent work on superspin-3/2 and superspin-1 multiplets. Superspin-3/2 multiplets contain component fields with spins (2, 3/2, 3/2, 1) and superspin-1 multiplets contain component fields with spins (3/2, 1, 1, 1/2). The super projector method is used to distinguish supersymmetric subspaces. Here, this method is used to write general superspace actions. The underlying geometrical structure of superspace actions is elucidated when they are written in terms of super projectors. This thesis also discusses the connection between four-dimensional massive theories and five-dimensional massless theories. This connection is understood in non-supersymmetric field theory but has not been established in superspace. A future direction of the five-dimensional models would involve finding an anti-de Sitter supergravity background. In order to construct this model using the knowledge gained from this thesis, an understanding of the Casimir operators of four-dimensional anti-de Sitter superspace would be necessary. These Casimir operators have not yet appeared in the literature and are presented in this thesis.