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Universe is considered as a brane in infinite (2+4)-space. It is shown that zero modes of all kinds of matter fields and 4-gravity are localized on the brane by increasing transversal gravitational potential.

We present a new 3-brane solution to Einstein's equations in (1+5)-spacetime with a negative bulk cosmological constant. This solution is a stringlike defect solution with decreasing scale function approaching a finite non-zero value in the radial infinity. It is shown that all local fields are localized on the brane only through the gravitational interaction. * Electronic address:

Growing non-singular solution of 6-dimensional Einstein equations for the 4-brane in infinite transversal 2-space is found. This solution provides gravitational trapping of matter and 4-dimensional gravity on the brane without extra delta-like source. The suitable solution exists in the case of the (2+4)-space and not exists for the (1+5)-signature. : 11.10.Kk, 04.50.+h, 11.25.Mj, 98.80.Cq After the papers [1, 2, 3] the models with brane-Universe in a high dimensional space-time have become popular. Large extra dimensions may play an important role in solving such problems as smallness of cosmological constant, the origin of the hierarchy, the nature of flavor, the source of SUSY breaking, etc. As in previous articles [3,4,5,6,7], in the present paper the Universe is considered as a single brane. PACSBrane models need some natural matter localization mechanism and explanation of 4-dimensional Newton's law. The question of matter localization on the brane has been investigated in various papers (for recent ideas see [8]). In our opinion the localizing force must be universal for all types of 4-dimensional matter fields. In our world gravity is known to be the unique interaction which has universal coupling with all matter fields. If extended extra dimensions exist, it is natural to assume that trapping of matter on the brane has a gravitational nature. Because of problems with quantum field theory in curve space it is difficult to find exact trapping mechanism for different matter fields separately. Our approach is more general: to provide universal and stable trapping we assume that on the brane (where all gravitating matter can reside) gravitational potential should have minimal value with respect to extra coordinates.Growing gravitational potential is the opposite choice compared to the one of Randall-Sundrum with the maximum on the brane [2]. We assume that 4-dimensional Newton's law on the brane is the result of the cancellation mechanism introduced in [3, 6] (as it is in Randall-Sundrum's case also), which allows both types of gravitational potential. This mechanism can be used even for a simple 5-dimensional model with exponentially growing transversal gravitational potential. Far from the brane (natural cutoff is the width of the brane) transversal gravitational potential becomes large and usual splitting of 5-dimensional space of [2,3,4,5] cannot be valid any more. This is similar to the case of QCD where nobody worries about the increasing quark potential.In this paper we introduce a realistic model of gravity and matter localization on (1+3)-brane embedded in a (2+4)-space in the case of growing transversal gravitational potential. Our motivation for the choice of the signature is as follows. In the massless field case (weakest coupling with gravity) symmetries of a multi-dimensional manifold can be restored. It is well known, that in the zero-mass limit the main equations of physics are invariant under the 15-parameter nonlinear conformal transformations. A long time ago it was also discovered that...