Four-dimensional gravity on a covariant noncommutative space
Abstract We formulate a model of noncommutative four-dimensional gravity on a covariant fuzzy space based on SO(1, 4), that is the fuzzy version of the dS4. The latter requires the employment of a wider symmetry group, the SO(1, 5), for reasons of covariance. Addressing along the lines of formulatin...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP08(2020)001 |
| _version_ | 1819174932810039296 |
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| author | G. Manolakos P. Manousselis G. Zoupanos |
| author_facet | G. Manolakos P. Manousselis G. Zoupanos |
| author_sort | G. Manolakos |
| collection | DOAJ |
| description | Abstract We formulate a model of noncommutative four-dimensional gravity on a covariant fuzzy space based on SO(1, 4), that is the fuzzy version of the dS4. The latter requires the employment of a wider symmetry group, the SO(1, 5), for reasons of covariance. Addressing along the lines of formulating four-dimensional gravity as a gauge theory of the Poincaré group, spontaneously broken to the Lorentz, we attempt to construct a four-dimensional gravitational model on the fuzzy de Sitter spacetime. In turn, first we consider the SO(1, 4) subgroup of the SO(1, 5) algebra, in which we were led to, as we want to gauge the isometry part of the full symmetry. Then, the construction of a gauge theory on such a noncommutative space directs us to use an extension of the gauge group, the SO(1, 5)×U(1), and fix its representation. Moreover, a 2-form dynamic gauge field is included in the theory for reasons of covariance of the transformation of the field strength tensor. Finally, the gauge theory is considered to be spontaneously broken to the Lorentz group with an extension of a U(1), i.e. SO(1, 3)×U(1). The latter defines the four-dimensional noncommutative gravity action which can lead to equations of motion, whereas the breaking induces the imposition of constraints that will lead to expressions relating the gauge fields. It should be noted that we use the Euclidean signature for the formulation of the above programme. |
| first_indexed | 2024-12-22T20:46:50Z |
| format | Article |
| id | doaj.art-01bf67d08f744e9eb23df5d6b7bbdb0b |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T20:46:50Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-01bf67d08f744e9eb23df5d6b7bbdb0b2022-12-21T18:13:12ZengSpringerOpenJournal of High Energy Physics1029-84792020-08-012020812910.1007/JHEP08(2020)001Four-dimensional gravity on a covariant noncommutative spaceG. Manolakos0P. Manousselis1G. Zoupanos2Physics Department, National Technical UniversityPhysics Department, National Technical UniversityPhysics Department, National Technical UniversityAbstract We formulate a model of noncommutative four-dimensional gravity on a covariant fuzzy space based on SO(1, 4), that is the fuzzy version of the dS4. The latter requires the employment of a wider symmetry group, the SO(1, 5), for reasons of covariance. Addressing along the lines of formulating four-dimensional gravity as a gauge theory of the Poincaré group, spontaneously broken to the Lorentz, we attempt to construct a four-dimensional gravitational model on the fuzzy de Sitter spacetime. In turn, first we consider the SO(1, 4) subgroup of the SO(1, 5) algebra, in which we were led to, as we want to gauge the isometry part of the full symmetry. Then, the construction of a gauge theory on such a noncommutative space directs us to use an extension of the gauge group, the SO(1, 5)×U(1), and fix its representation. Moreover, a 2-form dynamic gauge field is included in the theory for reasons of covariance of the transformation of the field strength tensor. Finally, the gauge theory is considered to be spontaneously broken to the Lorentz group with an extension of a U(1), i.e. SO(1, 3)×U(1). The latter defines the four-dimensional noncommutative gravity action which can lead to equations of motion, whereas the breaking induces the imposition of constraints that will lead to expressions relating the gauge fields. It should be noted that we use the Euclidean signature for the formulation of the above programme.http://link.springer.com/article/10.1007/JHEP08(2020)001Non-Commutative GeometryGauge SymmetryModels of Quantum Gravity |
| spellingShingle | G. Manolakos P. Manousselis G. Zoupanos Four-dimensional gravity on a covariant noncommutative space Journal of High Energy Physics Non-Commutative Geometry Gauge Symmetry Models of Quantum Gravity |
| title | Four-dimensional gravity on a covariant noncommutative space |
| title_full | Four-dimensional gravity on a covariant noncommutative space |
| title_fullStr | Four-dimensional gravity on a covariant noncommutative space |
| title_full_unstemmed | Four-dimensional gravity on a covariant noncommutative space |
| title_short | Four-dimensional gravity on a covariant noncommutative space |
| title_sort | four dimensional gravity on a covariant noncommutative space |
| topic | Non-Commutative Geometry Gauge Symmetry Models of Quantum Gravity |
| url | http://link.springer.com/article/10.1007/JHEP08(2020)001 |
| work_keys_str_mv | AT gmanolakos fourdimensionalgravityonacovariantnoncommutativespace AT pmanousselis fourdimensionalgravityonacovariantnoncommutativespace AT gzoupanos fourdimensionalgravityonacovariantnoncommutativespace |