Conformal geometry and (super)conformal higher-spin gauge theories

  title={Conformal geometry and (super)conformal higher-spin gauge theories},
  author={Sergei M. Kuzenko and Michael Ponds},
  journal={Journal of High Energy Physics},
A bstractWe develop a manifestly conformal approach to describe linearised (super)conformal higher-spin gauge theories in arbitrary conformally flat backgrounds in three and four spacetime dimensions. Closed-form expressions in terms of gauge prepotentials are given for gauge-invariant higher-spin (super) Cotton and (super) Weyl tensors in three and four dimensions, respectively. The higher-spin (super) Weyl tensors are shown to be conformal primary (super)fields in arbitrary conformal (super… 

Conformal interactions between matter and higher-spin (super)fields

In even spacetime dimensions, the interacting bosonic conformal higher-spin (CHS) theory can be realised as an induced action. The main ingredient in this definition is the model S[φ, h] describing a

Higher-spin Cotton tensors and massive gauge-invariant actions in AdS3

In a conformally flat three-dimensional spacetime, the linearised higher-spin Cotton tensor Cα(n)(h) is the unique conserved conformal current which is a gauge-invariant descendant of the conformal

New locally (super)conformal gauge models in Bach-flat backgrounds

For every conformal gauge field $h_{\alpha (n)\dot \alpha (m)}$ in four dimensions, with $n\geq m >0$, a gauge-invariant action is known to exist in arbitrary conformally flat backgrounds. If the

Duality-invariant superconformal higher-spin models

We develop a general formalism of duality rotations for bosonic conformal spin-s gauge fields, with s ≥ 2, in a conformally flat four-dimensional spacetime. In the s = 1 case this formalism is

Generalised conformal higher-spin fields in curved backgrounds

The problem of constructing gauge-invariant actions for conformal higher-spin fields in curved backgrounds is known to be notoriously difficult. In this paper we present gauge-invariant models for

AdS (super)projectors in three dimensions and partial masslessness

Abstract We derive the transverse projection operators for fields with arbitrary integer and half-integer spin on three-dimensional anti-de Sitter space, AdS3. The projectors are constructed in

AdS superprojectors

Within the framework of N = 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield Vα(m)α̇(n) :=

Matter-free higher spin gravities in 3D: Partially-massless fields and general structure

We study the problem of interacting theories with (partially)-massless and conformal higher spin fields without matter in three dimensions. A new class of theories that have partially-massless fields

Extended superconformal higher-spin gauge theories in four dimensions

Abstract Using the off-shell formulation for $$ \mathcal{N} $$ N = 2 conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved

New conformal higher spin gravities in 3d

We propose a new class of conformal higher spin gravities in three dimensions, which extends the one by Pope and Townsend. The main new feature is that there are infinitely many examples of the new



Higher spin conformal geometry in three dimensions and prepotentials for higher spin gauge fields

A bstractWe study systematically the conformal geometry of higher spin bosonic gauge fields in three spacetime dimensions. We recall the definition of the Cotton tensor for higher spins and establish

Lagrangian conformal higher spin theory

In a previous paper conformal gravity was derived by means of a precise action principle on the hypercone in the conformal space. Here it is shown that the same technique used to construct conformal

Conformal supergravity in five dimensions: new approach and applications

A bstractWe develop a new off-shell formulation for five-dimensional (5D) conformal supergravity obtained by gauging the 5D superconformal algebra in superspace. An important property of the

Off-shell higher spin N=2 supermultiplets in three dimensions

Off-shell higher spin N=2 supermultiplets in three spacetime dimensions (3D) are presented in this paper. We propose gauge prepotentials for higher spin superconformal gravity and construct the

Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields

A bstractWe introduce prepotentials for fermionic higher-spin gauge fields in four space-time dimensions, generalizing earlier work on bosonic fields. To that end, we first develop tools for handling

Superfield theories in tensorial superspaces and the dynamics of higher spin fields

We present the superfield generalization of free higher spin equations in tensorial superspaces and analyze tensorial supergravities with GL(n) and SL(n) holonomy as a possible framework for the

Weyl gauging and conformal invariance