The Gauge Theory of Weyl Group and its Interpretation as Weyl Quadratic Gravity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917934816821248 |
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| author | Condeescu, Cezar Micu, Andrei |
| author_facet | Condeescu, Cezar Micu, Andrei |
| contents | In this paper we give an extensive description of Weyl quadratic gravity as the gauge theory of the Weyl group. The previously discovered (vectorial) torsion/non-metricity equivalence is shown to be built-in as it corresponds to a redefinition of the generators of the Weyl group. We present a generalisation of the torsion/non-metricity duality which includes, aside from the vector, also a traceless 3-tensor with two antisymmetric indices and vanishing skew symmetric part. A discussion of this relation in the case of minimally coupled matter fields is given. We further point out that a Rarita-Schwinger field can couple minimally to all the components of torsion and some components of non-metricity. Alongside we present the same gauge construction for the Poincaré and conformal groups. We show that even though the Weyl group is a subgroup of the conformal group, the gauge theory of the latter is actually only a special case of Weyl quadratic gravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07159 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Gauge Theory of Weyl Group and its Interpretation as Weyl Quadratic Gravity Condeescu, Cezar Micu, Andrei High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology In this paper we give an extensive description of Weyl quadratic gravity as the gauge theory of the Weyl group. The previously discovered (vectorial) torsion/non-metricity equivalence is shown to be built-in as it corresponds to a redefinition of the generators of the Weyl group. We present a generalisation of the torsion/non-metricity duality which includes, aside from the vector, also a traceless 3-tensor with two antisymmetric indices and vanishing skew symmetric part. A discussion of this relation in the case of minimally coupled matter fields is given. We further point out that a Rarita-Schwinger field can couple minimally to all the components of torsion and some components of non-metricity. Alongside we present the same gauge construction for the Poincaré and conformal groups. We show that even though the Weyl group is a subgroup of the conformal group, the gauge theory of the latter is actually only a special case of Weyl quadratic gravity. |
| title | The Gauge Theory of Weyl Group and its Interpretation as Weyl Quadratic Gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2408.07159 |