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.


81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
Full Text: DOI arXiv


[1] Snyder, H.S., Phys. rev., 71, 38, (1947)
[2] DeWitt, B.S., Phys. rev. lett., 13, 114, (1964)
[3] Yoneya, T., Prog. theor. phys., 56, 1310, (1976)
[4] Padmanabhan, T.; Padmanabhan, T., Ann. phys. (N.Y.), Class. quantum grav., 4, L107, (1987)
[5] Garay, L.J., Int. J. mod. phys. A, 10, 145, (1995)
[6] Ashtekar, A.; Rovelli, C.; Smolin, L.; Rovelli, C., Phys. rev. lett., Nucl. phys. B, 405, 797, (1993)
[7] Padmanabhan, T.; Padmanabhan, T.; Padmanabhan, T., Phys. rep., Mod. phys. lett. A, 17, 1147, (2002) · Zbl 1012.83025
[8] Padmanabhan, T.; Padmanabhan, T.; Seshadri, T.R.; Singh, T.P., Phys. rev. lett., Phys. rev. D, 39, 2100, (1989)
[9] Chouha, P.H.; Brandenberger, R.H.
[10] Padmanabhan, T.; Padmanabhan, T., Phys. rev. lett., Phys. rev. D, 57, 6206, (1998)
[11] Padmanabhan, T.; Padmanabhan, T.; Srinivasan, K.; Sriramkumar, L.; Padmanabhan, T.; Shankaranarayanan, S.; Padmanabhan, T., Phys. rev. lett., Phys. rev. D., Phys. rev. D., Int. J. mod. phys. D, 10, 351, (2001)
[12] Hatfield, B.; Polchinski, J.; Zwiebach, B., A first course in string theory, Cambridge monographs on mathematical physics, (2004), Cambridge Univ. Press Cambridge
[13] Jain, S.; Patil, S.P.; Brandenberger, R., Phys. rev. D, 71, 103522, (2005)
[14] Smailagic, A.; Spallucci, E.; Padmanabhan, T.
[15] Spallucci, E.; Fontanini, M., Zero-point length, extra-dimensions and string T-duality, ()
[16] Antoniadis, I.; Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G.; Shiu, G.; Tye, S.-H.H.; Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G., Phys. lett. B, Phys. rev. D, Phys. rev. D, 59, 086004, (1999)
[17] Cremades, D.; Ibanez, L.E.; Marchesano, F.; Kokorelis, C., Nucl. phys. B, Nucl. phys. B, 677, 115, (2004)
[18] Hossenfelder, S.; Bleicher, M.; Hofmann, S.; Ruppert, J.; Scherer, S.; Stocker, H.; Harbach, U.; Hossenfelder, S.; Bleicher, M.; Stoecker, H.; Hossenfelder, S.; Hossenfelder, S., Phys. lett. B, Phys. lett. B, Phys. lett. B, Phys. rev. D, 70, 105003, (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.