Variations on a theme of MacDowell-Mansouri
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911538203328512 |
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| author | Alvarez, P. D. Krasnov, K. |
| author_facet | Alvarez, P. D. Krasnov, K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21930 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variations on a theme of MacDowell-Mansouri Alvarez, P. D. Krasnov, K. Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | Variations on a theme of MacDowell-Mansouri |
| topic | Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.21930 |