Abstract
Three families of solutions of the background field equations for the bosonic string are presented. These solutions describe a D-dimensional space-time for which the constant time slices are tori with D −1 “rolling radii” - that is, radii which are allowed to vary with time, along with a time-dependent dilation field. Each of the three families (which correspond to D = 26, D > 26, or D < 26) includes solutions where d radii increase as the other D− d−1 radii decrease, where 0⩽ d⩽ D − 1. It is shown that these solutions can be extended to order α' in nonlinear sigma model perturbation theory, and it is conjectured that this continues to any given order in α'.
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