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

Sergei M. Kuzenko, Michael Ponds

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We 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)gravity backgrounds, however they are gauge invariant only if the background (super) Weyl tensor vanishes. The proposed higher-spin actions are (super) Weyl-invariant on arbitrary curved backgrounds, however the appropriate higher-spin gauge invariance holds only in the conformally flat case. We also describe conformal models for generalised gauge fields that are used to describe partially massless dynamics in three and four dimensions. In particular, generalised higher-spin Cotton and Weyl tensors are introduced.

Original languageEnglish
Article number113
JournalJournal of High Energy Physics
Volume2019
Issue number5
DOIs
Publication statusPublished - 1 May 2019

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gauge theory
geometry
tensors
cotton
gauge invariance
gravitation

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title = "Conformal geometry and (super)conformal higher-spin gauge theories",
abstract = "We 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)gravity backgrounds, however they are gauge invariant only if the background (super) Weyl tensor vanishes. The proposed higher-spin actions are (super) Weyl-invariant on arbitrary curved backgrounds, however the appropriate higher-spin gauge invariance holds only in the conformally flat case. We also describe conformal models for generalised gauge fields that are used to describe partially massless dynamics in three and four dimensions. In particular, generalised higher-spin Cotton and Weyl tensors are introduced.",
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Conformal geometry and (super)conformal higher-spin gauge theories. / Kuzenko, Sergei M.; Ponds, Michael.

In: Journal of High Energy Physics, Vol. 2019, No. 5, 113, 01.05.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Conformal geometry and (super)conformal higher-spin gauge theories

AU - Kuzenko, Sergei M.

AU - Ponds, Michael

PY - 2019/5/1

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AB - We 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)gravity backgrounds, however they are gauge invariant only if the background (super) Weyl tensor vanishes. The proposed higher-spin actions are (super) Weyl-invariant on arbitrary curved backgrounds, however the appropriate higher-spin gauge invariance holds only in the conformally flat case. We also describe conformal models for generalised gauge fields that are used to describe partially massless dynamics in three and four dimensions. In particular, generalised higher-spin Cotton and Weyl tensors are introduced.

KW - Higher Spin Gravity

KW - Higher Spin Symmetry

KW - Supergravity Models

KW - Superspaces

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JO - Journal of High Energy Physics

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