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

@article{Kuzenko2019ConformalGA, title={Conformal geometry and (super)conformal higher-spin gauge theories}, author={Sergei M. Kuzenko and Michael Ponds}, journal={Journal of High Energy Physics}, year={2019}, volume={2019}, pages={1-59} }

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…

## 23 Citations

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

- Physics
- 2022

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

- Mathematics
- 2021

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

- Physics
- 2020

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

- Physics, MathematicsPhysical Review D
- 2021

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

- Mathematics
- 2019

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

- MathematicsJournal of High Energy Physics
- 2021

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

- Physics, Mathematics
- 2021

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

- Mathematics
- 2020

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

- Physics, MathematicsJournal of High Energy Physics
- 2021

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

- PhysicsJournal of High Energy Physics
- 2020

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…

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