Vortices on the World Sheet and String's Critical Dynamics

摘要

Non-perturbative effects in the first quantized string propagating in non-simply connected space are considered. These effects are due to vortices on the string world sheet, which have to appear in properly regularized two-dimensional field theory describing the world sheet's dynamics. Owing to this critical indices, in particular the critical dimensions, continuously depend on external parameters such as radii of non-simply connected circles or temperature. The strings on the lattices are discussed and the dynamical reasons for self dual lattices are suggested. It is shown that non-positively definite lattices, such as a hyperbollic, can be described as an antiferromagnetics in the formalism of functional integral. The critical dynamics on non-simply connected orbifolds and Calabi-Yau manifolds are shortly considered. The two new issues are: the field condensate mechanism different from Hosotani one, and the open question about the real dimension of compact manifold. 12 refs.; 2 figs. (Atomindex citation 19:037374)