English

Variations on a theme of MacDowell-Mansouri

Differential Geometry 2026-03-24 v1 General Relativity and Quantum Cosmology High Energy Physics - Theory

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.

Keywords

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

R2 v1 2026-07-01T11:33:15.552Z