Large and infinite extra dimensions

Theoretical studies on more than three spatial dimensions are currently showing a distinct shift toward the 'brane world' picture, in which ordinary matter (with the possible exceptions of gravitons and hypothetical particles interacting very weakly with matter) is within a three-dimensional submanifold - brane - embedded in a multi-dimensional space. The extra dimensions may be large and indeed infinite and may show up directly in current or future experiments. In the present paper the basic ideas of the brane theory are presented in an accessible way using simple field-theoretical models.