2020/09/30 by Samuel Brensinger, Kenneth Heitritter, V.G.J. Rodgers +2 · 7 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebra over a field #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Covariant transformation #Diffeomorphism #Gauge theory #Geodesic #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #String theory #Virasoro algebra #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.103.044060
published in Physical review. D/Physical review. D. 103(4) (American Physical Society) · 52 pages. Made revisions for acceptance to the journal Physical Review D
arxiv created 2021/01/22 · openalex publication_date 2021/02/25 · arxiv updated 2021/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Thomas-Whitehead (TW) gravity is a projectively invariant model of gravity over a d-dimensional manifold that is intimately related to string theory through reparametrization invariance. Unparametrized geodesics are the ubiquitous structure that ties together string theory and higher dimensional gravitation. This is realized through the projective geometry of Tracy Thomas. The projective connection, due to Thomas and later Whitehead, admits a component that in one dimension is in one-to-one correspondence with the coadjoint elements of the Virasoro algebra. This component is called the diffeomorphism field Dab in the literature. It also has been shown that in four dimensions, the TW action collapses to the Einstein-Hilbert action with cosmological constant when Dab is proportional to the Einstein metric. These previous results have been restricted to either particular metrics, such as the Polyakov 2D metric, or were restricted to coordinates that were volume preserving. In this paper, we review TW gravity and derive the gauge invariant TW action that is explicitly projectively invariant and general coordinate invariant. We derive the covariant field equations for the TW action and show how fermionic fields couple to the gauge invariant theory. The independent fields are the metric tensor gab, the fundamental projective invariant \mathrm\ensuremathΠabc, and the diffeomorphism field Dab.