Gravity from AKSZ-Manin theories in two, three, and four dimensions

Leron Borsten; Dimitri Kanakaris; Hyungrok Kim

doi:10.1007/jhep06(2025)075

Gravity from AKSZ-Manin theories in two, three, and four dimensions

Leron Borsten, Dimitri Kanakaris, Hyungrok Kim

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Abstract

We show that various dynamical gauge theories in two, three and four dimensions, obtained as Manin deformations of topological Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) theories, are equivalent to gravitational theories. Since gravity is topological in two and three dimension, this equivalence requires a diffeomorphism breaking background source term. In four dimensions, however, the MacDowell-Mansouri formulation of Einstein gravity with a cosmological constant is obtained identically via the Manin deformation of a particular AKSZ theory.

Original language	English
Article number	75
Pages (from-to)	1-17
Number of pages	17
Journal	Journal of High Energy Physics (JHEP)
Volume	2025
Issue number	6
Early online date	9 Jun 2025
DOIs	https://doi.org/10.1007/jhep06(2025)075
Publication status	E-pub ahead of print - 9 Jun 2025

Keywords

Gauge Symmetry
Classical Theories of Gravity
Chern-Simons Theories
de Sitter space

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10.1007/jhep06(2025)075Licence: CC BY

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© 2025 The Author(s). This is an open access article distributed under the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/
Final published version, 373 KBLicence: CC BY

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abstract = "We show that various dynamical gauge theories in two, three and four dimensions, obtained as Manin deformations of topological Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) theories, are equivalent to gravitational theories. Since gravity is topological in two and three dimension, this equivalence requires a diffeomorphism breaking background source term. In four dimensions, however, the MacDowell-Mansouri formulation of Einstein gravity with a cosmological constant is obtained identically via the Manin deformation of a particular AKSZ theory.",

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AB - We show that various dynamical gauge theories in two, three and four dimensions, obtained as Manin deformations of topological Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) theories, are equivalent to gravitational theories. Since gravity is topological in two and three dimension, this equivalence requires a diffeomorphism breaking background source term. In four dimensions, however, the MacDowell-Mansouri formulation of Einstein gravity with a cosmological constant is obtained identically via the Manin deformation of a particular AKSZ theory.

KW - Gauge Symmetry

KW - Classical Theories of Gravity

KW - Chern-Simons Theories

KW - de Sitter space

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Gravity from AKSZ-Manin theories in two, three, and four dimensions

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Keywords

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