### Abstract

The MacDowell-Mansouri formulation of general relativity is based on a gauge theory whose gauge algebra depends on the sign of the cosmological constant. In this article, we show that the gauge algebra is uniquely determined by the conformal structure of spacetime itself. Specifically, we show that in vacuum: the spacetime conformal holonomy algebra coincides with the MacDowell-Mansouri gauge algebra for both signs of the cosmological constant, in both Lorentzian and Euclidean metric signatures.

Original language | English |
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Article number | 032501 |

Number of pages | 14 |

Journal | Journal of Mathematical Physics |

Volume | 55 |

Issue number | 3 |

Early online date | 10 Mar 2014 |

DOIs | |

Publication status | Published - 2014 |

### Keywords

- general relativity
- conformal geometry
- MacDowell-Mansouri gravity

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## Profiles

### Charles Wang

Person: Academic

## Cite this

Reid, J. A., & Wang, C. H-T. (2014). Conformal holonomy in MacDowell-Mansouri gravity.

*Journal of Mathematical Physics*,*55*(3), [032501]. https://doi.org/10.1063/1.4867337