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arXiv · 2603.21930

Variations on a theme of MacDowell-Mansouri

P. D. Alvarez·K. Krasnov
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Abstract

Inspired by the MacDowell-Mansouri formulation of four-dimensional General Relativity, we study a class of four-dimensional gauge-theoretic functionals obtained from the Pontryagin density of a G-connection by inserting, under the trace, a matrix that breaks the gauge group G to a subgroup H. Concretely, we study the model with the pair (G,H) given by (SU(3), U(2)). We show that the critical points of the resulting functional are constant scalar curvature almost-Kahler 4-manifolds. On compact 4-manifolds, a stronger conclusion holds under the additional assumption that the scalar curvature is non-negative and the first Chern class is such that an Einstein metric can exist. In this case, results in the literature imply that the critical points are Kahler-Einstein 4-manifolds.

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P. D. Alvarez, K. Krasnov. 2026-03-23. Variations on a theme of MacDowell-Mansouri. https://arxiv.org/abs/2603.21930

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