String Theory and Space-Time Uncertainty Principle
Abstract
The notion of a space-time uncertainty principle in string theory is clarified and further developed. The motivation and the derivation of the principle are first reviewed in a reasonably self-contained way. It is then shown that the nonperturbative (Borel summed) high-energy and high-momentum transfer behavior of string scattering is consistent with the space-time uncertainty principle. It is also shown that, as a consequence of this principle, string theories in 10 dimensions generically exhibit a characteristic length scale which is equal to the well-known 11 dimensional Planck length gs1/3ls of M-theory as the scale at which stringy effects take over the effects of classical supergravity, even without involving D-branes directly. The implications of the space-time uncertainty relation in connection with D-branes and black holes are discussed and reinterpreted. Finally, we present a novel interpretation of the Schild-gauge action for strings from the viewpoint of noncommutative geometry. This conforms to the space-time uncertainty relation by manifestly exhibiting a noncommutativity of quantized string coordinates between, dominantly, space and time. We also discuss the consistency of the space-time uncertainty relation with S and T dualities.
- Publication:
-
Progress of Theoretical Physics
- Pub Date:
- June 2000
- DOI:
- 10.1143/PTP.103.1081
- arXiv:
- arXiv:hep-th/0004074
- Bibcode:
- 2000PThPh.103.1081Y
- Keywords:
-
- High Energy Physics - Theory
- E-Print:
- 45 pages, 1 figure, remaining typos corrected, further typos of published version are corrected