  We revisit a non-perturbative formulation leading to a vacuum created
gravitational pair of (33)-brane by a Poincare dual higher form U (1) gauge
theory on a D4 -brane. In particular, the analysis has revealed a dynamical
geometric torsion H 3 for an on-shell Neveu-Schwarz (NS) form on a fat 4-brane.
We argue that a D-instanton can be a viable candidate to incorporate the
quintessence correction hidden to an emergent (3 + 1)-dimensional brane
universe. It is shown that a dynamical non-perturbative correction may be
realized with an axionic scalar QFT on an emergent anti 3-brane within a
gravitational pair. The theoretical tool provokes thought to believe for an
extra instantaneous dimension transverse to our classical brane-universe in an
emergent scenario. Interestingly a D-instanton correction, sourced by an axion
on an anti 3-brane, may serve as a potential candidate to explain the
accelerated rate of expansion of our 3-brane universe and may provide a clue to
the origin of dark energy.
