Abstract
We revisit a five dimensional Kaluza-Klein gravity, in presence of a cosmological constant, with a renewed interest in a type IIA string theory. An irreducible space-time curvature scalar K, leading to a non-perturbation theory of emergent quantum gravity, is addressed on a D4-brane underlying a two form gauge theory. An appropriate ansatz for a two form in the non-linear U (1) gauge theory is explored to obtain a nontrivial geometric torsion in a second order formalism. The quantum geometries, underlying torsion, in a low energy limit is shown to describe an AdS5 -brane black hole in Einstein vacuum. In the limit, we analyze the non-perturbation curvature K on S1 and argue for a plausible strong-weak coupling duality between a five dimensional non-perturbation curvature theory and the 4D perturbation non-linear gauge theory.
Highlights
An intrinsic notion of geometry, governing space-time curvature, is manifested beautifully in the success of the General Theory of Relativity (GTR)
With the help of an extra dimension to Einstein vacuum, the matter/geometry relation may be explored to view as a gauge/gravity duality or in particular AdS5-gravity/gauge theory duality established in literatures [1,2,3]
Since a flat space is not associated with any holographic direction, it is promising to begin with Newtonian potential to describe the emergent gravity phenomenon as a non-relativistic limit of GTR
Summary
An intrinsic notion of geometry, governing space-time curvature, is manifested beautifully in the success of the General Theory of Relativity (GTR). The external geometries on a D-brane sourced by a zero mode of a two form may be exploited further to address some of the non-external quantum black holes underlying generalized non-perturbation formalism. A non-zero vacuum energy density sourced by a nonzero energy momentum tensor in the formalism may allow the emergent curvature theory of torsion to be compared with Einstein gravity in presence of a cosmological constant. The conformal invariance in the quantum world-sheet theory is known to describe an effective closed string action in ten dimensional space-time which includes a three form gauge curvature. In order to address a space-time curvature from a gauge theoretic, we exploit the two form gauge connections to appropriately modify the covariant derivative in a second order formalism
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