Weyl gauge invariant DBI action in conformal geometry
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929748023705600 |
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| author | Ghilencea, D. M. |
| author_facet | Ghilencea, D. M. |
| contents | We construct the analogue of the Dirac-Born-Infeld (DBI) action in Weyl conformal geometry in $d$ dimensions and obtain a general theory of gravity with Weyl gauge symmetry of dilatations (Weyl-DBI). This is done in the Weyl gauge covariant formulation of conformal geometry in $d$ dimensions, suitable for a gauge theory, in which this geometry is metric. The Weyl-DBI action is a special gauge theory in that it has the same gauge invariant expression with dimensionless couplings in any dimension $d$, with no need for a UV regulator (be it a DR subtraction scale, field or higher derivative operator) for which reason we argue it is Weyl-anomaly free. For $d=4$ dimensions, the leading order of a series expansion of the Weyl-DBI action recovers the gauge invariant Weyl quadratic gravity action associated to this geometry, that is Weyl anomaly-free; this is broken spontaneously and Einstein-Hilbert gravity is recovered in the broken phase, with $Λ>0$. All the remaining terms of this series expansion are of non-perturbative nature but can, in principle, be recovered by (perturbative) quantum corrections in Weyl quadratic gravity in $d=4$ in a gauge invariant (geometric) regularisation, provided by the Weyl-DBI action. If the Weyl gauge boson is not dynamical the Weyl-DBI action recovers in the leading order the conformal gravity action. All fields and scales have geometric origin, with no added matter, scalar field compensators or UV regulators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weyl gauge invariant DBI action in conformal geometry Ghilencea, D. M. High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We construct the analogue of the Dirac-Born-Infeld (DBI) action in Weyl conformal geometry in $d$ dimensions and obtain a general theory of gravity with Weyl gauge symmetry of dilatations (Weyl-DBI). This is done in the Weyl gauge covariant formulation of conformal geometry in $d$ dimensions, suitable for a gauge theory, in which this geometry is metric. The Weyl-DBI action is a special gauge theory in that it has the same gauge invariant expression with dimensionless couplings in any dimension $d$, with no need for a UV regulator (be it a DR subtraction scale, field or higher derivative operator) for which reason we argue it is Weyl-anomaly free. For $d=4$ dimensions, the leading order of a series expansion of the Weyl-DBI action recovers the gauge invariant Weyl quadratic gravity action associated to this geometry, that is Weyl anomaly-free; this is broken spontaneously and Einstein-Hilbert gravity is recovered in the broken phase, with $Λ>0$. All the remaining terms of this series expansion are of non-perturbative nature but can, in principle, be recovered by (perturbative) quantum corrections in Weyl quadratic gravity in $d=4$ in a gauge invariant (geometric) regularisation, provided by the Weyl-DBI action. If the Weyl gauge boson is not dynamical the Weyl-DBI action recovers in the leading order the conformal gravity action. All fields and scales have geometric origin, with no added matter, scalar field compensators or UV regulators. |
| title | Weyl gauge invariant DBI action in conformal geometry |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2407.18173 |