Zero-point length from string fluctuations

One of the leading candidates for quantum gravity, viz. string theory, has the following features incorporated in it. (i) The full spacetime is higher-dimensional, with (possibly) compact extra-dimensions; (ii) there is a natural minimal length below which the concept of continuum spacetime needs to be modified by some deeper concept. On the other hand, the existence of a minimal length (zero-point length) in four-dimensional spacetime, with obvious implications as UV regulator, has been often conjectured as a natural aftermath of any correct quantum theory of gravity. We show that one can incorporate the apparently unrelated pieces of information-zero-point length, extra-dimensions, string T-duality-in a consistent framework. This is done in terms of a modified Kaluza-Klein theory that interpolates between (high-energy) string theory and (low-energy) quantum field theory. In this model, the zero-point length in four dimensions is a “virtual memory” of the length scale of compact extra-dimensions. Such a scale turns out to be determined by T-duality inherited from the underlying fundamental string theory. From a low energy perspective short distance infinities are cutoff by a minimal length which is proportional to the square root of the string slope, i.e., α′. Thus, we bridge the gap between the string theory domain and the low energy arena of point-particle quantum field theory.