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Zero-point length from string fluctuations. (English) Zbl 1247.81369
Summary: One of the leading candidates for quantum gravity, namely 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 a UV regulator, has often been conjectured as a natural consequence 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., $$\sqrt{\alpha'}$$. Thus, we bridge the gap between the string theory domain and the low-energy arena of point-particle quantum field theory.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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