We revisit the effective space-time torsion curvature in a second order formalism, underlying the non-linear U (1) gauge dynamics, of a two form on a D 4 -brane. The formalism incorporates a significant global NS two form into the theory via its perturbative coupling to a dynamical two form. In particular we explore the non-linear gauge dynamics on a D 4 -brane in the presence of a non-trivial background metric. An effective de Sitter universe is shown to emerge on a vacuum created pair of (DD) 3 -branes by a local two form at the past horizon with the Big Bang. We obtain a number of 4D de Sitter quantum black holes with and without a propagating torsion. In a low energy limit the non-perturbative correction may be seen to be insignificant. The quantum black hole undergoes an expansion in the limit and identifies with the Einstein vacuum. Interestingly our analysis reveals a plausible quintessence (axion) on an anti-D 3 -brane which may source the dark energy in a D 3 -brane universe. Arguably a brane universe moves away from its anti-brane due to the conjectured repulsive gravity underlying the quintessence. It leads to a growth in the extra fifth dimension between a brane and an anti-brane, which may provide a clue to an accelerating universe as observed in cosmology.

We obtain a Schwarzschild and a Reissner-Nordstrom emergent black holes, by exploring the torsion dynamics in a generalized curvature formulation, underlying an effective D4-brane on S 1 . It is shown that a constant effective metric, sourced by a background fluctuation in B2-potential, on a D3-brane receives a dynamical quantum correction in presence of an electric charge.

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We investigate some of the quantum gravity effects on a vacuum created pair of (DD) 3 -brane by a non-linear U (1) gauge theory on a D 4 -brane. In particular we obtain a four dimensional quantum Kerr(Newman) black hole in an effective torsion curvature formalism sourced by a two form dynamics in the world-volume of a D 4 -brane on S 1 . Interestingly the event horizon is found to be independent of a non-linear electric charge and the 4D quantum black hole is shown to describe a degenerate vacua in string theory. We show that the quantum Kerr brane universe possesses its origin in a de Sitter vacuum. In a nearly S 2 -symmetric limit the Kerr geometries may seen to describe a Schwarzschild and Reissner-Nordstrom quantum black holes. It is argued that a quantum Reissner-Nordstrom tunnels to a large class of degenerate Schwazschild vacua. In a low energy limit the non-linear electric charge becomes significant at the expense of the degeneracies. In the limit the quantum geometries may identify with the semi-classical black holes established in Einstein gravity. Analysis reveals that a quantum geometry on a vacuum created D 3 -brane universe may be described by a low energy perturbative string vacuum in presence of a nonperturbative quantum correction.