GLOBAL STRINGS IN EXTRA DIMENSIONS: THE FULL MAP OF SOLUTIONS, MATTER TRAPPING, AND THE HIERARCHY PROBLEM
Bronnikov K.A., Meierovich B.E.

Received: August 6, 2007

PACS: 04.50.+h, 11.27.+d

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We consider (d₀+2)-dimensional configurations with global strings in two extra dimensions and a flat metric in d₀ dimensions, endowed with a warp factor e^2γ depending on the distance l from the string center. All possible regular solutions of the field equations are classified by the behavior of the warp factor and the extra-dimensional circular radius r(l). Solutions with r→ ∞ and r→const>0 as l→ ∞ are interpreted in terms of thick brane-world models. Solutions with r → 0 as l → l_c >0, i.e., those with a second center, are interpreted as either multi-brane systems (which is appropriate for large enough distances l_c between the centers) or as Kaluza-Klein-type configurations with extra dimensions invisible due to their smallness. In the case of the Mexican-hat symmetry-breaking potential, we build the full map of regular solutions on the (\eps, Γ) parameter plane, where \eps acts as an effective cosmological constant and Γ characterizes the gravitational field strength. The trapping properties of candidate brane worlds for test scalar fields are discussed. Good trapping properties for massive fields are found for models with increasing warp factors. Kaluza-Klein-type models are shown to have nontrivial warp factor behaviors, leading to matter particle mass spectra that seem promising from the standpoint of hierarchy problems.