The BRST Double Complex for the Coupling of Gravity to Gauge Theories
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914168888623104 |
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| author | Prinz, David |
| author_facet | Prinz, David |
| contents | We consider (effective) Quantum General Relativity coupled to the Standard Model (QGR-SM) and clarify whether graviton-ghosts couple to matter particles. To this end, we examine the corresponding BRST and anti-BRST symmetries, which are generated by infinitesimal diffeomorphisms and infinitesimal gauge transformations. In particular, we study their properties and relations: We find that all differentials mutually anticommute, which implies that they form a double complex. In particular, we introduce the total BRST differential as the sum of the diffeomorphism and gauge BRST differentials and similarly the total anti-BRST differential as the sum of the respective anti-BRST differentials. Furthermore, we identify the functionals in particle fields that are (co)cycles up to total derivatives with respect to the diffeomorphism differentials as scalar tensor densities of weight one: This implies that graviton-ghosts decouple from matter particles if and only if the Yang--Mills gauge fixing Lagrange density has said tensor density weight. Moreover, we discuss the relevant gauge fixing fermions: Starting from the de Donder and Lorenz gauge fixing conditions, we introduce a total gauge fixing fermion that generates the complete gauge fixing and ghost Lagrange density of QGR-SM. Finally, we show that the BRST cocomplexes are isomorphic to their corresponding anti-BRST complexes via ghost conjugation. Notably, this relates the BRST cohomologies to their respective anti-BRST homologies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2206_00780 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The BRST Double Complex for the Coupling of Gravity to Gauge Theories Prinz, David High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics 81T13, 81T70, 83C47 We consider (effective) Quantum General Relativity coupled to the Standard Model (QGR-SM) and clarify whether graviton-ghosts couple to matter particles. To this end, we examine the corresponding BRST and anti-BRST symmetries, which are generated by infinitesimal diffeomorphisms and infinitesimal gauge transformations. In particular, we study their properties and relations: We find that all differentials mutually anticommute, which implies that they form a double complex. In particular, we introduce the total BRST differential as the sum of the diffeomorphism and gauge BRST differentials and similarly the total anti-BRST differential as the sum of the respective anti-BRST differentials. Furthermore, we identify the functionals in particle fields that are (co)cycles up to total derivatives with respect to the diffeomorphism differentials as scalar tensor densities of weight one: This implies that graviton-ghosts decouple from matter particles if and only if the Yang--Mills gauge fixing Lagrange density has said tensor density weight. Moreover, we discuss the relevant gauge fixing fermions: Starting from the de Donder and Lorenz gauge fixing conditions, we introduce a total gauge fixing fermion that generates the complete gauge fixing and ghost Lagrange density of QGR-SM. Finally, we show that the BRST cocomplexes are isomorphic to their corresponding anti-BRST complexes via ghost conjugation. Notably, this relates the BRST cohomologies to their respective anti-BRST homologies. |
| title | The BRST Double Complex for the Coupling of Gravity to Gauge Theories |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics 81T13, 81T70, 83C47 |
| url | https://arxiv.org/abs/2206.00780 |