Abhishek K. Singh, K. Priyabrat Pandey, Sunita Singh, Supriya Kar
The U(1) gauge dynamics on a $D_4$-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 quantum fluctuation into an effective $D_4$-brane. Interestingly, the near horizon $D_4$-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 emergent mixed dS patches to describe a Schwazschild-like dS (SdS) and a topological-like dS (TdS) black holes. We analyze the Hawking radiations from a SdS vacuum to arrive at a Nariai geometry, where the discrete torsion forms a condensate. We perform thermal analysis to identify a Nariai vacuum with a TdS, where the condensate tunnels down to a stable AdS, underlying an effective $D_4$-brane. Investigation reveals an AdS patch within a thermal dS brane and may provide clue to unfold dS/CFT. On the other hand, the role of dark energy, sourced by a discrete torsion, in the dS vacua is investigated using Painleve geometries. It is argued that an instanton pair (D-brane and anti D-brane) is created by a discrete torsion, with a Big Bang/Crunch, at the past horizon in a pure dS vacuum. Nucleation, of brane/anti-brane pair(s), is qualitatively analyzed to construct an effective space-time on a $D_4$-brane and its anti brane. Analysis presumably re-assures the significant role played by the non-zero modes, in NS-NS two form, to generalize the notion of branes within a brane.
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http://arxiv.org/abs/1303.4344
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