Dirac and Faddeev-Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension

Escalante, Alberto; Zárate, Moisés

doi:10.48550/arxiv.1406.4430

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“…In fact, the tachyon condensate proposed by A. Sen [28] presents an additional difficulty due to the complex form of the field equations, however, despite these difficulties, in a recent work [27], an interesting and novel solution which localizes 4D gravity using a real tachyon field was obtained. Subsequently, the localization of gauge vector fields in this braneworld was recently accomplished and reported in the literature [29] (see [30] as well for an alternative mechanism for localizing gauge and Kalb-Ramond fields on thick branes based on a 5D Stueckelberg action, and [31]- [32] for its canonical quantization). A peculiar feature of this expanding thick braneworld model is that both the gravitational and gauge vector fields only possess a single massless bound state localized on the 3-brane in their corresponding mass spectra, allowing us to successfully recover the phenomenology of our 4D world.…”

Section: Introduction and Review Of The Modelmentioning

confidence: 99%

On localization of universal scalar fields in a tachyonic de Sitter thick braneworld

et al. 2014

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Braneworld models may yield interesting effects ranging from high-energy physics to cosmology, or even some low-energy physics. Their mode structure modifies standard results in these physical realms that can be tested and used, for example, to set bounds on the models parameters. Now, to define braneworld deviations from standard 4D physics, a notion of matter and gravity localization on the brane is crucial. In this work we investigate the localization of universal massive scalar fields in a de Sitter thick tachyonic braneworld generated by gravity coupled to a tachyonic bulk scalar field. This braneworld possesses a 4D de Sitter induced metric and is asymptotically flat despite the presence of a negative bulk cosmological constant, a novel and interesting peculiarity that contrasts with previously known models. It turns out that universal scalar fields can be localized in this expanding braneworld if their bulk mass obeys an upper bound, otherwise the scalar fields delocalize: The dynamics of the scalar field is governed by a Schrödinger equation with an analog quantum mechanical potential of modified Pöschl-Teller type. This potential depends on the bulk curvature of the braneworld system as well as on the value of the bulk scalar field mass. For masses satisfying a certain upper bound, the potential displays a negative minimum and possesses a single massless bound state separated from the Kaluza-Klein (KK) massive modes by a mass gap defined by the Hubble (expansion scale) parameter of the 3-brane. As the bulk scalar field mass increases, the minimum of the quantum mechanical potential approaches a null value and, when the bulk mass reaches certain upper bound, it becomes positive (eventually transforming into a potential barrier), leading to delocalization of the bulk scalar field from the brane. We present analytical expressions for the general solution of the Schrödinger equation. Thus, the KK massive modes are given in terms of general Heun functions as well as the expression for the massless zero mode, giving rise to a new application of these special functions.

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