Large and infinite extra dimensions

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Abstract
The emphasis in the developmet of theories with more than three spatial dimensions has recently shifted towards ``brane world'' picture, which assumes that ordinary matter (with possible exceptions of gravitons and other, hypothetic, particles which interact very weakly with matter) is trapped to a three-dimensional submanifold --- brane --- embedded in fundamental multi-dimensional space. In the brane world scenario, extra dimensions may be large, and even infinite; they may have effects, directly observable in current or fothcoming experiments. On the basis of simple field-theoretic models, various ideas in this direction are exposed at a non-expert level.Comment: 55 pages, 10 figures Several references and figures added. Journal version, to appear in Uspekhi Fiz. Nau

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