p-forms on the celestial sphere

Donnay, Laura; Esmaeili, Erfan; Heissenberg, Carlo

doi:10.21468/SciPostPhys.15.1.026

SciPost Physics

p-forms on the celestial sphere

Laura Donnay, Erfan Esmaeili, Carlo Heissenberg

SciPost Phys. 15, 026 (2023) · published 25 July 2023

doi: 10.21468/SciPostPhys.15.1.026
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Abstract

We construct a basis of conformal primary wavefunctions (CPWs) for $p$-form fields in any dimension, calculating their scalar products and exhibiting the change of basis between conventional plane wave and CPW mode expansions. We also perform the analysis of the associated shadow transforms. For each family of $p$-form CPWs, we observe the existence of pure gauge wavefunctions of conformal dimension $\Delta=p$, while shadow $p$-forms of this weight are only pure gauge in the critical spacetime dimension value $D=2p+2$. We then provide a systematic technique to obtain the large-$r$ asymptotic limit near $\mathscr I$ based on the method of regions, which naturally takes into account the presence of both ordinary and contact terms on the celestial sphere. In $D=4$, this allows us to reformulate in a conformal primary language the links between scalars and dual two-forms.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.1.026
TI  - p-forms on the celestial sphere
PY  - 2023/07/25
UR  - https://www.scipost.org/SciPostPhys.15.1.026
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 1
SP  - 026
A1  - Donnay, Laura
AU  - Esmaeili, Erfan
AU  - Heissenberg, Carlo
AB  - We construct a basis of conformal primary wavefunctions (CPWs) for $p$-form fields in any dimension, calculating their scalar products and exhibiting the change of basis between conventional plane wave and CPW mode expansions. We also perform the analysis of the associated shadow transforms. For each family of $p$-form CPWs, we observe the existence of pure gauge wavefunctions of conformal dimension $\Delta=p$, while shadow $p$-forms of this weight are only pure gauge in the critical spacetime dimension value $D=2p+2$. We then provide a systematic technique to obtain the large-$r$ asymptotic limit near $\mathscr I$ based on the method of regions, which naturally takes into account the presence of both ordinary and contact terms on the celestial sphere. In $D=4$, this allows us to reformulate in a conformal primary language the links between scalars and dual two-forms.
ER  -

@Article{10.21468/SciPostPhys.15.1.026,
	title={{p-forms on the celestial sphere}},
	author={Laura Donnay and Erfan Esmaeili and Carlo Heissenberg},
	journal={SciPost Phys.},
	volume={15},
	pages={026},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.1.026},
	url={https://scipost.org/10.21468/SciPostPhys.15.1.026},
}

Cited by 5

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¹ ² Laura Donnay,
³ Erfan Esmaeili,
⁴ ⁵ Carlo Heissenberg

Funders for the research work leading to this publication

Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
Instituto Nazionale di Fisica Nucleare (INFN) (through Organization: Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN])
Knut och Alice Wallenbergs Stiftelse (Knut and Alice Wallenberg Foundation) (through Organization: Knut och Alice Wallenbergs Stiftelse / Knut and Alice Wallenberg Foundation)
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