Zero-point length from string fluctuations

TL;DR

This paper presents a framework linking string theory, extra dimensions, and zero-point length in spacetime, showing how string T-duality determines a minimal length scale that regularizes quantum field theory at short distances.

Contribution

It introduces a modified Kaluza-Klein model that unifies string T-duality, extra dimensions, and zero-point length into a consistent low-energy effective theory.

Findings

Zero-point length is related to the size of compact extra dimensions.

T-duality determines the minimal length scale in four-dimensional spacetime.

The minimal length scale is proportional to the square root of the string slope .

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 (or 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 cut off by a minimal length which is proportional to the square root of the string slope, i.e. \sqrt{\alpha^\prime}. Thus, we bridge the gap between the string theory domain and the low energy arena of point-particle quantum field theory.