Geometric torsion, four-form, Riemann duals and Quintessence

We revisit an emergent gravity scenario in (4+1) dimensions underlying a propagating geometric torsion Script capital H3 with a renewed interest. We show that a pair-symmetric 4th-order curvature tensor is sourced by Neveu-Schwarz (NS) two-form in a U(1) 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 4th-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 U(1) 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 d = 12 emergent form theory. Investigation reveals that a pair of (MM)10-brane is created across an event horizon. We show that an emergent M theory in a decoupling limit identifies with the bosonic sector of N = 1, Supergravity in d = 11.