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.
Bibliographical noteWe are grateful to Graham Hall for helpful discussions. J.R. acknowledges an EPSRC Ph.D. Studentship (EP/I036877/1.)
- general relativity
- conformal geometry
- MacDowell-Mansouri gravity