General structure of Thomas-Whitehead gravity
| Autor: | Samuel Brensinger, Kenneth Heitritter, Kory Stiffler, Vincent G. J. Rodgers |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
High Energy Physics - Theory Geodesic 010308 nuclear & particles physics FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) String theory 01 natural sciences Invariant theory General Relativity and Quantum Cosmology High Energy Physics::Theory High Energy Physics - Theory (hep-th) 0103 physical sciences Projective connection Virasoro algebra Covariant transformation Diffeomorphism 010306 general physics Mathematical physics Projective geometry |
| Zdroj: | Physical Review |
| Popis: | Thomas-Whitehead (TW) gravity is a projectively invariant model of gravity over a d-dimensional manifold that is intimately related to string theory through reparameterization invariance. Unparameterized 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 $\mathcal{D}_{ab }$ 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 $\mathcal{D}_{ab}$ 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 $g_{ab}$, the fundamental projective invariant $\Pi^{a}_{\,\,\,bc}$, and the diffeomorphism field $\mathcal D_{ab}$. Comment: 52 pages. Made revisions for acceptance to the journal Physical Review D |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|