Higgs mechanism for the Ashtekar self-dual connection
Abstract We introduce the Higgs mechanism for the self-dual spin connection (also known as the Ashtekar connection), using the Plebański formulation of gravity. We develop our formalism within the framework of the chiral action and derive the equations of motion of the theory. One particular test mo...
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| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-14497-z |
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| _version_ | 1849234567744978944 |
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| author | Bruno Alexandre |
| author_facet | Bruno Alexandre |
| author_sort | Bruno Alexandre |
| collection | DOAJ |
| description | Abstract We introduce the Higgs mechanism for the self-dual spin connection (also known as the Ashtekar connection), using the Plebański formulation of gravity. We develop our formalism within the framework of the chiral action and derive the equations of motion of the theory. One particular test model is explored: since anisotropy is an intrinsic property of the theory, a modified version of the spatially flat Bianchi I model with two different scale factors is considered. We apply our formalism and derive the Friedmann equations which regulate the scale factors and the Higgs field. We also present a Proca-like term for the connection, which when reduced to minisuperspace with a positive $$\Lambda $$ Λ yields a De Sitter universe with an effective cosmological constant that depends on the mass of the gauge fields. We finally investigate the effect of these mass terms on gravitational waves and find that the wave equation remains unchanged relatively to GR; however the Weyl tensor is scaled by a constant which depends on the mass of the connection components. |
| format | Article |
| id | doaj-art-d3c1a1587b1c4d4c8e9d0b728dd9eca9 |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-d3c1a1587b1c4d4c8e9d0b728dd9eca92025-08-20T04:03:06ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-07-018571710.1140/epjc/s10052-025-14497-zHiggs mechanism for the Ashtekar self-dual connectionBruno Alexandre0Theoretical Physics Group, Imperial CollegeAbstract We introduce the Higgs mechanism for the self-dual spin connection (also known as the Ashtekar connection), using the Plebański formulation of gravity. We develop our formalism within the framework of the chiral action and derive the equations of motion of the theory. One particular test model is explored: since anisotropy is an intrinsic property of the theory, a modified version of the spatially flat Bianchi I model with two different scale factors is considered. We apply our formalism and derive the Friedmann equations which regulate the scale factors and the Higgs field. We also present a Proca-like term for the connection, which when reduced to minisuperspace with a positive $$\Lambda $$ Λ yields a De Sitter universe with an effective cosmological constant that depends on the mass of the gauge fields. We finally investigate the effect of these mass terms on gravitational waves and find that the wave equation remains unchanged relatively to GR; however the Weyl tensor is scaled by a constant which depends on the mass of the connection components.https://doi.org/10.1140/epjc/s10052-025-14497-z |
| spellingShingle | Bruno Alexandre Higgs mechanism for the Ashtekar self-dual connection European Physical Journal C: Particles and Fields |
| title | Higgs mechanism for the Ashtekar self-dual connection |
| title_full | Higgs mechanism for the Ashtekar self-dual connection |
| title_fullStr | Higgs mechanism for the Ashtekar self-dual connection |
| title_full_unstemmed | Higgs mechanism for the Ashtekar self-dual connection |
| title_short | Higgs mechanism for the Ashtekar self-dual connection |
| title_sort | higgs mechanism for the ashtekar self dual connection |
| url | https://doi.org/10.1140/epjc/s10052-025-14497-z |
| work_keys_str_mv | AT brunoalexandre higgsmechanismfortheashtekarselfdualconnection |