Variations on a theme of MacDowell-Mansouri
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.
Cite
@article{arxiv.2603.21930,
title = {Variations on a theme of MacDowell-Mansouri},
author = {P. D. Alvarez and K. Krasnov},
journal= {arXiv preprint arXiv:2603.21930},
year = {2026}
}
Comments
25 pages, no figures