Determining the dual

摘要: We study the R -> 0 limit for heterotic strings of either kind (Spin(32)/Z_2 or E_8 x E_8) compactified on a circle, in presence an arbitrary Wilson line. Though generic line this leads to chaotic behaviour, there are two distinguished, countable subsets lines, that dense total space lines: One subset decompactification limits; second converges onto periodic orbits. Many implications carry over circle small but finite radius. To complete picture, we discuss global aspects moduli-space, compare it with ``fiducial'' moduli-space type I give derivation map between moduli string theories at point space, and compute smallest radius can be probed.