Discrete torsion, de Sitter tunneling vacua and AdS brane: U(1) gauge
  theory on D4-brane and an effective curvature
  The U(1) gauge dynamics on a D4-brane is revisited, with a two form, to
construct an effective curvature theory in a second order formalism. We exploit
the local degrees in a two form, and modify its dynamics in a gauge invariant
way, to incorporate a non-perturbative metric fluctuation in an effective
D4-brane. Interestingly, the near horizon D4-brane is shown to describe an
asymptotic Anti de Sitter (AdS) in a semi-classical regime. Using Weyl
scaling(s), we obtain the emergent rotating geometries leading to primordial de
Sitter (dS) and AdS vacua in a quantum regime. Under a discrete transformation,
we re-arrange the mixed dS patches to describe a Schwazschild-like dS (SdS) and
a topological-like dS (TdS) black holes. We analyze SdS vacuum for Hawking
radiations to arrive at Nariai geometry, where a discrete torsion forms a
condensate. We perform thermal analysis to identify Nariai vacuum with a TdS.
Investigation reveals an AdS patch within a thermal dS brane, which may provide
a clue to unfold dS/CFT. In addition, the role of dark energy, sourced by a
discrete torsion, in the dS vacua is investigated using Painleve geometries. It
is argued that a D-instanton pair is created by a discrete torsion, with a Big
Bang/Crunch, at the past horizon in a pure dS. Nucleation, of brane/anti-brane
pair(s), is qualitatively analyzed to construct an effective space-time on a
D4-brane and its anti brane. Analysis re-assures the significant role played by
a non-zero mode, of NS-NS two form, to generalize the notion of branes within a
brane.
