Presymplectic BV-AKSZ formulation of conformal gravity

Ivan Dneprov; Maxim Grigoriev

doi:10.1140/epjc/s10052-022-11082-6

2022 Impact factor 4.4

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 6
https://doi.org/10.1140/epjc/s10052-022-11082-6

Regular Article - Theoretical Physics

Presymplectic BV-AKSZ formulation of conformal gravity

Ivan Dneprov¹^,2 and Maxim Grigoriev¹^,2^b

¹ Lebedev Physical Institute, Leninsky Ave. 53, 119991, Moscow, Russia
² Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University, 119991, Moscow, Russia

^b grig@lpi.ru

Received: 23 October 2022
Accepted: 25 November 2022
Published online: 7 January 2023

Abstract

We elaborate on the presymplectic BV-AKSZ approach to local gauge theories and apply it to conformal gravity. More specifically, we identify a compatible presymplectic structure on the minimal model of the total BRST complex of this theory and show that together with the BRST differential it determines a full-scale BV formulation for a specific frame-like action which seems to be previously unknown. Remarkably, the underlying frame-like description requires no artificial off-shell constraints. Instead, the action becomes equivalent to the usual conformal gravity one, upon gauging away all the variables belonging to the kernel of the presymplectic structure. Finally, we show how the presymplectic BV-AKSZ approach extends to generic gauge theories.

© The Author(s) 2023

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