Quantum effects in topological and Schwarzschild de Sitter brane: Aspects of torsion on ${\mathbf{(D{\bar D})_4}}$-brane universe

TL;DR

This paper explores how quantum torsion effects influence the geometry and dynamics of brane universes, leading to emergent gravity, topological de Sitter and Schwarzschild branes, and connections to higher-dimensional superstring theories.

Contribution

It introduces a novel formalism for analyzing torsion in D-branes, linking quantum effects to emergent gravity and brane universe geometries in six dimensions.

Findings

Emergent gravity describes a low energy string vacuum with quantum corrections.

Topological de Sitter and Schwarzschild brane universes are derived in six dimensions.

Brane/anti-brane geometries exhibit characteristic thermal behaviors influenced by quantum effects.

Abstract

We investigate an effective torsion curvature in a second order formalism underlying a two form world-volume dynamics in a $D_5$-brane. In particular, we consider the two form in presence of a background (open string) metric in a $U(1)$ gauge theory. Interestingly the formalism may be viewed via a non-coincident pair of $(D{\bar D})_5$-brane with a global NS two form on an anti brane and a local two form on a brane. The energy-momentum tensor is computed in the six dimensional CFT. It is shown to source a metric fluctuation on a vacuum created pair of $(D{\bar D})_4$-brane at a cosmological horizon by the two form quanta in the gauge theory. The emergent gravity scenario is shown to describe a low energy (perturbative) string vacuum in $6D$ with a (non-perturbative) quantum correction by a lower ($p<5$) dimensional $D_p$ brane or an anti brane in the formalism. A closed string exchange between a pair of $(D{\bar D})_4$-brane, underlying a closed/open string duality, is argued to describe the Einstein vacuum in a low energy limit. We obtain topological de Sitter and Schwarzschild brane universe in six dimensions. The brane/anti-brane geometries are analyzed to explore some of their characteristic and thermal behaviours in presence of the quantum effects. They reveal an underlying nine dimensional type IIA and IIB superstring theories on $S^1$.