Zero-point length from string fluctuations

Abstract

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.