Localization of Matter and Cosmological Constant on a Brane in Anti de Sitter Space

TL;DR

This work analyzes how matter fields of spins 0, 1/2, and 3/2, as well as the 4D cosmological constant, can localize on a 3-brane in ${\rm AdS}_5$ with RS-like warp factors. It shows that spin-0 scalars localize on a positive-tension brane with a localized zero-mode plus a continuum of states, while vector fields do not localize in the minimal setup; spin-1/2 and spin-3/2 fermions localize on a negative-tension brane, and spin-1/2 can localize on a positive-tension brane with extra interactions. A key result is that fine-tuning between the bulk cosmological constant and brane tension can be avoided by introducing a non-propagating four-form gauge field, whose constant field strength shifts the effective cosmological constant and yields a continuous family of brane Universes, including one with zero effective 4D cosmological constant. This framework has implications for brane-world phenomenology and holographic interpretations, and it opens the door to anthropic considerations by allowing multiple possible ${\\Lambda_4}$ values for generic bulk parameters.

Abstract

We study two issues, the localization of various spin fields, and the problem of the cosmological constant on a brane in five-dimensional anti de Sitter space. We find that spin-zero fields are localized on a positive-tension brane. In addition to the localized zero-mode there is a continuous tower of states with no mass gap. Spin one-half and three-half states can be localized on a brane with ``negative tension''. Their localization can be achieved on the positive-tension brane as well, if additional interactions are introduced. The necessary ingredient of the scenario with localized gravity is the relation between the bulk cosmological constant and the brane tension. In the absence of supersymmetry this implies fine-tuning between the parameters of the theory. To deal with this issue we introduce a four-form gauge field. This gives an additional arbitrary contribution to the bulk cosmological constant. As a result, the model gives rise to a continuous family of brane Universe solutions for generic values of the bulk cosmological constant and the brane tension. Among these solutions there is one with a zero four-dimensional cosmological constant.