Abstract
Spin 1/2 fields localization on an asymmetric dS${}_4$ scenario, where the brane interpolates between two spacetimes dS${}_5$ and AdS${}_5$, is determined. The bulk spinor is coupled to scalar field of the brane by a nonminimal Yukawa term compatible with the scenario's geometry. We show that, independently of wall's thickness, only one massless chiral mode is localized on the wall. The massive chiral modes follow a Schr\"odinger equation, whose potential has a mass gap determined by Yukawa constant, which is a generic property of this system. The fermions spectrum is defined bellow the gap, by bound states of both chiralities with the same mass, and above the gap, by a continuous spectrum with local and global resonant modes of both chiralities and different mass.
Highlights
A de-Sitter brane corresponds to a dynamic hypersurface with positive curvature embedded in a higher dimensional spacetime, e.g., five dimensions
The cosmological constant on the dS4 brane generates, in the effective potential of the bulk fluctuations, a massive gap that always favors the capture of massless graviton
The brane can be obtained as a pair vacuum solutions to the Einstein equations rigidly connected on a slice of the bulk [1,11] or as the thin-wall limit of a domain wall, which is a solution to the coupled Einstein-Klein Gordon system, where the scalar field interpolates between the minima of a self-interaction potential [12,13,14]
Summary
A de-Sitter (dS4) brane corresponds to a dynamic hypersurface with positive curvature embedded in a higher dimensional spacetime, e.g., five dimensions. In [23], a proposal to construct a nonminimal Yukawa coupling in compatibility with the scenario’s geometry was presented Under this mechanism, the fermions localization takes place via the warp factor of scenario, as happens with the gravitational fluctuations, and as a consequence it is possible to keep the matter field coupled to the wall even in the limit of zero thickness. The minimal coupling case, ΦðφÞ 1⁄4 φ, has been widely discussed in several opportunities and for a dS4 scenario it has been proved insufficient to find normalizable solutions for the zero mode [19], because asymptotically the metric factor and scalar field behave like eAðzÞ → 0 and φ → φÆ, respectively, which implies that u ∼ 1 as jzj → ∞, in agreement with (16). This pairing of the mass eigenmodes is required for the existence of massive fermions satisfying (12)
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