^{3}

We show that the massless form fields in

The general theory of relativity (GTR) is governed by a metric tensor dynamics in 4D underlying a pseudo-Riemannian manifold. The GTR is a second-order formulation and is geometric. It describes an interacting classical theory and hence it rules out the possibility of a perturbation quantum theory. Furthermore, the coupled nature of differential field equations in GTR ensures non-linear solutions, which are believed to be sourced by an appropriate energy–momentum tensor possibly underlying a non-linear gauge field. Thus, the quantum field dynamical correction to GTR demands a non-perturbation (NP) formulation at second order.

Einstein gravity is believed to be an emergent phenomenon that is not fundamental but rather a low-energy limit of some theory [

It has also been shown that gravity can emerge from a gauge theory in non-commutative (NC) spacetime, which further implies that gravity is a composite picture that emerges from gauge fields in a fuzzy spacetime [

Interestingly, the theoretical requirement has been attempted with a dynamical geometric torsion

In this article we present an elegant tool to generate mass for a gauge field by a geometric torsion in a

In the context, a Dirichlet

However, the mathematical difficulties do not allow an arbitrary NS field to couple to an open string boundary, though it is known to describe a torsion in 10 dimensions. A torsion is shown to modify the covariant derivative and hence the effective curvatures in a superstring theory [

The stringy pair production by the KR form primarily generalizes the established Schwinger pair production mechanism [

In particular, the stringy pair production by the KR quanta has been explored in diversified contexts to obtain: (i) a degenerate Kerr [

We begin with the KR form

The

We begin with an NP theory of emergent gravity in

Equivalently, the emergent theory may be described by the geometric form(s). We set

The first term in all three actions of Eqs. (

A geometric

The geometric two-form in an emergent non-perturbation theory, Eq. (

At first sight the emergent curvature tensor

It can be checked that

The relation between an NP theory like Eq. (

Potential variation shows that a non-perturbative stable vacuum may be viewed as a perturbative unstable vacuum.

In a gauge choice for a non-propagating geometric torsion, the gauge-theoretic

At this juncture we recall a transition from the KR gauge theory on a

The dynamical correspondence is primarily between a KR form in the world-volume gauge theory and an NS form in superstring theory. Equation (

The dynamical correspondence between a perturbative gauge theory and a non-perturbative emergent gravity is remarkable. It signifies a strong/weak coupling duality [

A realization of the perturbative vacuum of Eq. (

The first term in the bulk topological action is a total divergence. However, it regains significance at the

The emergent gravity scenarios [

The NP idea leading to mass generation suggests that a dynamical axion (quintessence) or generically a higher essence is hidden to an emergent

We begin by recalling the perspectives of a CFT underlying a KR gauge theory on a

Interestingly, the local degrees of an NS field in

The complex scalar field

The interaction energy function

Thus a large number of stable ground/vacuum states, underlying the local

A shift from an unstable (a non-perturbation) vacuum, Eq. (

This implies that a cosmological constant appears to possess its origin in the symmetry-breaking phase and is sourced by the Higgs mechanism. Keeping track of the four local degrees in

The gauge field on an emergent

In an NP decoupling limit a gravitational

Furthermore, the emergent gravity on a

Four local degrees in

A mass for an NS field in the action of Eq. (

On the other hand, the topological term in Eq. (

Thus the Higgs scalar in an NP-decoupling limit ensures a small cosmological constant. Analysis suggests that the Einstein–Hilbert action in the presence of a small non-zero value for

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