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General structure of Thomas-Whitehead gravity
Journal article   Open access   Peer reviewed

General structure of Thomas-Whitehead gravity

Samuel Brensinger, Kenneth Heitritter, Vincent G. J. Rodgers and Kory Stiffler
Physical review. D, Vol.103(4), 044060
02/25/2021
DOI: 10.1103/PhysRevD.103.044060
url
https://doi.org/10.1103/PhysRevD.103.044060View
Published (Version of record) Open Access

Abstract

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 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 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 D-ab.
 Physical Sciences Physics Astronomy & Astrophysics Physics, Particles & Fields Science & Technology

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