Conformal symmetry in quantum gravity
Abstract We study the problem of how to derive conformal symmetry in the framework of quantum gravity. We start with a generic gravitational theory which is invariant under both the general coordinate transformation (GCT) and Weyl transformation (or equivalently, local scale transformation), and the...
| المؤلف الرئيسي: | |
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| التنسيق: | مقال |
| اللغة: | English |
| منشور في: |
SpringerOpen
2024-09-01
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| سلاسل: | European Physical Journal C: Particles and Fields |
| الوصول للمادة أونلاين: | https://doi.org/10.1140/epjc/s10052-024-13240-4 |
| _version_ | 1826970802393710592 |
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| author | Ichiro Oda |
| author_facet | Ichiro Oda |
| author_sort | Ichiro Oda |
| collection | DOAJ |
| description | Abstract We study the problem of how to derive conformal symmetry in the framework of quantum gravity. We start with a generic gravitational theory which is invariant under both the general coordinate transformation (GCT) and Weyl transformation (or equivalently, local scale transformation), and then construct its BRST formalism by fixing the gauge symmetries by the extended de Donder gauge and scalar gauge conditions. These gauge-fixing conditions are invariant under global GL(4) and global scale transformations. The gauge-fixed and BRST invariant quantum action possesses a huge Poincaré-like IOSp(10|10) global symmetry, from which we can construct an extended conformal symmetry in a flat Minkowski background in the sense that the Lorentz symmetry is replaced with the GL(4) symmetry. Moreover, we construct the conventional conformal symmetry out of this extended symmetry. With a flat Minkowski background $$\langle g_{\mu \nu } \rangle = \eta _{\mu \nu }$$ ⟨ g μ ν ⟩ = η μ ν and a non-zero scalar field $$\langle \phi \rangle \ne 0$$ ⟨ ϕ ⟩ ≠ 0 , the GL(4) and global scale symmetries are spontaneously broken to the Lorentz symmetry, thereby proving that the graviton and the dilaton are respectively the corresponding Nambu–Goldstone bosons, and therefore they must be exactly massless at nonperturbative level. One of remarkable aspects in our findings is that in quantum gravity, a derivation of conformal symmetry does not depend on a classical action, and its generators are built from only the gauge-fixing and the FP ghost actions. Finally, we address a generalized Zumino theorem in quantum gravity. |
| first_indexed | 2025-02-18T04:54:01Z |
| format | Article |
| id | doaj.art-d5d916a7280b498b9c901b640f8cbb90 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2025-02-18T04:54:01Z |
| publishDate | 2024-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-d5d916a7280b498b9c901b640f8cbb902024-11-17T12:44:58ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522024-09-0184911810.1140/epjc/s10052-024-13240-4Conformal symmetry in quantum gravityIchiro Oda0Department of Physics, Faculty of Science, University of the RyukyusAbstract We study the problem of how to derive conformal symmetry in the framework of quantum gravity. We start with a generic gravitational theory which is invariant under both the general coordinate transformation (GCT) and Weyl transformation (or equivalently, local scale transformation), and then construct its BRST formalism by fixing the gauge symmetries by the extended de Donder gauge and scalar gauge conditions. These gauge-fixing conditions are invariant under global GL(4) and global scale transformations. The gauge-fixed and BRST invariant quantum action possesses a huge Poincaré-like IOSp(10|10) global symmetry, from which we can construct an extended conformal symmetry in a flat Minkowski background in the sense that the Lorentz symmetry is replaced with the GL(4) symmetry. Moreover, we construct the conventional conformal symmetry out of this extended symmetry. With a flat Minkowski background $$\langle g_{\mu \nu } \rangle = \eta _{\mu \nu }$$ ⟨ g μ ν ⟩ = η μ ν and a non-zero scalar field $$\langle \phi \rangle \ne 0$$ ⟨ ϕ ⟩ ≠ 0 , the GL(4) and global scale symmetries are spontaneously broken to the Lorentz symmetry, thereby proving that the graviton and the dilaton are respectively the corresponding Nambu–Goldstone bosons, and therefore they must be exactly massless at nonperturbative level. One of remarkable aspects in our findings is that in quantum gravity, a derivation of conformal symmetry does not depend on a classical action, and its generators are built from only the gauge-fixing and the FP ghost actions. Finally, we address a generalized Zumino theorem in quantum gravity.https://doi.org/10.1140/epjc/s10052-024-13240-4 |
| spellingShingle | Ichiro Oda Conformal symmetry in quantum gravity European Physical Journal C: Particles and Fields |
| title | Conformal symmetry in quantum gravity |
| title_full | Conformal symmetry in quantum gravity |
| title_fullStr | Conformal symmetry in quantum gravity |
| title_full_unstemmed | Conformal symmetry in quantum gravity |
| title_short | Conformal symmetry in quantum gravity |
| title_sort | conformal symmetry in quantum gravity |
| url | https://doi.org/10.1140/epjc/s10052-024-13240-4 |
| work_keys_str_mv | AT ichirooda conformalsymmetryinquantumgravity |