Superspin projection operators and off-shell higher-spin supermultiplets on Minkowski and anti-de Sitter superspace

TL;DR

This thesis develops explicit superspin projection operators on various superspaces and explores their applications in higher-spin superconformal theories and massless higher-spin models with AdS supersymmetry.

Contribution

It provides explicit forms of superspin projectors in multiple superspace backgrounds and analyzes their role in higher-spin superconformal and gauge theories, including off-shell decompositions.

Findings

Explicit superspin projectors are constructed for diverse superspaces.

Higher-spin theories with (1,1) AdS supersymmetry decompose into (1,0) supermultiplets.

New off-shell higher-spin gauge models are identified and classified.

Abstract

This thesis is dedicated to the study of (super)spin projection operators and their applications on maximally symmetric (super)space backgrounds in three and four dimensions. On such backgrounds, the irreducible representations of the associated isometry (super)algebra may be realised on the space of tensor (super)fields satisfying certain differential constraints. The (super)spin projectors isolate the component of an unconstrained (super)field which furnishes the irreducible representation with maximal (super)spin. The explicit form of these (super)projectors are found in the following backgrounds: three-dimensional ($3d$) $\mathcal{N}$-extended Minkowski superspace $\mathbb{M}^{3|2 \mathcal{N}}$; $3d$ (anti-)de Sitter space (A)dS$_3$; $3d$ $\mathcal{N} = 1$ anti-de Sitter superspace AdS$^{3|2}$; four-dimensional ($4d$) $\mathcal{N} = 1$ anti-de Sitter superspace AdS$^{4|4}$; and $4d$ $\mathcal{N} = 2$ anti-de Sitter superspace AdS$^{4|8}$. An array of novel applications are investigated, with an emphasis placed on the interplay between (super)projectors and (super)conformal higher-spin theory. Another major component of this thesis consists of a detailed study of massless higher-spin gauge models with $\mathcal{N} = 2$ AdS supersymmetry in three dimensions. We find that every known higher-spin theory with $(1, 1)$ AdS supersymmetry decomposes into a sum of two off-shell $(1, 0)$ supermultiplets which belong to three series of inequivalent higher-spin gauge models.