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 Zero-point length from string fluctuations

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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.

Author: Michele Fontanini; Euro Spallucci; T. Padmanabhan


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