Circular strings, wormholes, and minimum size

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The quantization of circular strings in an anti-de Sitter background spacetime is performed, obtaining a discrete spectrum for the string mass. A comparison with a four-dimensional homogeneous and isotropic spacetime coupled to a conformal scalar field shows that the string radius and the scale factor have the same classical solutions and that the quantum theories of these two models are formally equivalent. However, the physically relevant observables of these two systems have different spectra, although they are related to each other by a specific one-to-one transformation. We finally obtain a discrete spectrum for the spacetime size of both systems, which presents a nonvanishing lower bound.
© 1997 The American Physical Society. The authors want to thank C. Barceló for helpful discussions. L.J.G. was supported by funds provided by DGICYT and MEC (Spain) under Contract Adjunct to the Project No. PB94-0107. P.G.-D. acknowledges DGICYT for financial support under Research Projects Nos. PB94-0107 and PB93-0139, and MEC Spanish German Joint Action No. 161.B. G.A.M.M. has been partially supported by funds provided by MEC and DGICYT under Research Project No. PB93-0139.
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