Geometric torsion, four-form, Riemann duals and Quintessence

Abstract

We revisit an emergent gravity scenario in [Formula: see text][Formula: see text][Formula: see text] dimensions underlying a propagating geometric torsion [Formula: see text] with a renewed interest. We show that a pair-symmetric [Formula: see text]th-order curvature tensor is sourced by Neveu–Schwarz (NS) two-form in a [Formula: see text] gauge theoretic formulation. Interestingly, the new spacetime curvature governs a torsion-free geometry sourced by an NS form and shares the properties of the Riemann tensor. On the other hand, a completely anti-symmetric [Formula: see text]th-order tensor in the formulation is shown to incorporate a dynamical geometric torsion and is argued to be identified with a nonperturbative correction. The four-form turns out to be [Formula: see text] gauge invariant underlying an onshell NS form. We show that an emergent gravity theory may elegantly be described with an axionic scalar presumably signifying a quintessence coupling to the Riemann-type geometries. The curvatures are appropriately worked out to obtain a [Formula: see text] emergent form theory. Investigation reveals that a pair of [Formula: see text]-brane is created across an event horizon. We show that an emergent [Formula: see text] theory in a decoupling limit identifies with the bosonic sector of [Formula: see text], Supergravity in [Formula: see text].