How do dimensions in string theory interact?
Well one thing you don't often see discussed is that the 6-dimensional manifolds (Calabi-Yau or whatever) that the extra dimensions are compacted on are actually complex 3-dimensional manifolds. A complex dimension is two real dimensions plus some structure. And there's plenty of string research on that structure.
String theory seems to have the best of general relativity (curvature) and quantum mechanics (discreteness). I guess that geodesics exhibit finite, quantized uncertainty at the Planck scale over dimensions of interval and dynamics, and there may resolve as piecewise sinusoidal strings under interdimensional Fourier transform. John Archibald Wheeler was prescient of such artifacts as strings in his "pregeometry."
Separate names with a comma.