Mass generation from a non-perturbative correction: Massive Neveu-Schwarz field and graviton in (3+1) dimensions

We show that the massless form fields in $(4+1)$-dimensional non-perturbation theory of emergent gravity become massive in a perturbative phase without the Higgs mechanism. In particular, an axionic scalar sourced by a non-perturbative dynamical correction is absorbed by the form fields to describe a massive Neveu-Schwarz (NS) field theory on an emergent gravitational $\left(3\overline{3}\right)$-brane pair. Arguably the novel idea of the Higgs mechanism is naturally invoked in an emergent gravity underlying a ${CFT}_6$. Analysis reveals "gravito-weak" and "electro-weak" phases respectively on a vacuum pair in $(4+1)$ and $(3+1)$ dimensions. It is argued that the massive NS field quanta may govern an emergent graviton on a gravitational $3$-brane.