Description
Many different formulations of general relativity are known. The Palatini action, based on a Lorentz connection and tetrad, can be derived from the MacDowell-Mansouri action, which combines these variables into a Cartan connection. The latter is obtained via gauge fixing and thus explicit symmetry breaking of the Stelle-West action to retain only Lorentz symmetry; the latter enlarges the Lorentz gauge symmetry of the Palatini action to the de Sitter or anti de Sitter groups. A different formulation is the Plebanski action, which is obtained from the Palatini action by a decomposition of the complexified Lorentz algebra into its self-dual and anti-self-dual parts. In my talk I will show how the aforementioned reformulations of the Palatini action can be cast into a common form by lifting these actions to a spin bundle and embedding the Lorentz algebra into its corresponding Clifford algebra, which is further embedded into the de Sitter or anti de Sitter Clifford algebra. In particular, I will show how this leads to a novel formulation of the Plebanski action, which does not need complexification, and retains the larger symmetry of the Stelle-West action, as both can be obtained with the help of spontaneous symmetry breaking and self-dual / anti-self-dual split within the enlarged Clifford algebra instead. This new formulation invites for interesting generalizations, in particular non-minimally coupled spinor fields, scalar field couplings and symmetry breaking similar to the Higgs mechanism.
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Manuel Hohmann (University of Tartu)30/06/2026, 11:001Oral talk
Many different formulations of general relativity are known. The Palatini action, based on a Lorentz connection and tetrad, can be derived from the MacDowell-Mansouri action, which combines these variables into a Cartan connection. The latter is obtained via gauge fixing and thus explicit symmetry breaking of the Stelle-West action to retain only Lorentz symmetry; the latter enlarges the...
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