Abstract
Dictated by Symmetry Principle, string theory predicts not General Relativity but its own gravity which assumes the entire closed string massless sector to be geometric and thus gravitational. In terms of R/(MG), i.e. the dimensionless radial variable normalized by mass, Stringy Gravity agrees with General Relativity toward infinity, but modifies it at short distance. At far short distance, gravitational force can be even repulsive. These may solve the dark matter and energy problems, as they arise essentially from small R/(MG) observations: long distance divided by much heavier mass. We address the pertinent differential geometry for Stringy Gravity, stringy Equivalence Principle, stringy geodesics and the minimal coupling to the Standard Model. We highlight the notion of ‘doubled-yet-gauged’ coordinate system, in which a gauge orbit corresponds to a single physical point and proper distance is defined between two gauge orbits by a path integral.
Highlights
Ever since Einstein formulated his theory of gravity, i.e. General Relativity (GR), the metric, gμν, has been privileged to be the only geometric and gravitational field, on account of the adopted
Forming the massless sector of closed strings, they are ubiquitous in all string theories, with the conventional (Riemannian) description given by dD x
A genuine stringy symmetry, called T-duality, can mix three of them [1, 2]. These may well hint at the existence of Stringy Gravity which should take the entire closed string massless sector to be geometric and gravitational
Summary
Ever since Einstein formulated his theory of gravity, i.e. General Relativity (GR), the metric, gμν, has been privileged to be the only geometric and gravitational field, on account of the adopted. A genuine stringy symmetry, called T-duality, can mix three of them [1, 2] These may well hint at the existence of Stringy Gravity which should take the entire closed string massless sector to be geometric and gravitational. The word ‘double’ refers to the fact that doubled (D +D)-dimensional coordinates are used for the description of Ddimensional physical spacetime While such a usage was historically first made in the case of a torus background – by introducing a dual coordinate conjugate to the string winding momentum – the doubled coordinates turned out to be far more general: they can be applied to any compact or non-compact spacetime, as well as to string and to particle physics
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