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Title:
From Virasoro to Thomas-Whitehead
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Abstract:
In 2D, Einstein’s classical theory of general relativity becomes trivial. Yet when one studies the symmetries of 2D through string theory, a new field, dubbed the diffeomorphism field, arise from the Virasoro algebra. We show that this field has meaning in higher dimensions through the ubiquitous notion projective connections that is also present in the symmetry of geodesics. By using the Thomas-Whitehead connection, which is a natural connection for projective geometry, we construct an action that gives the diffeomorphism field dynamics in the accompaniment of the Einstein-Hilbert action. From there we are able to describe how this field augments gravitational interactions with fermions and how it might be a component of dark energy and dark matter in 4D.
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