Details

Autor(en) / Beteiligte

• Pollock, M.D.

Titel

On the relationship between quantum cosmology and the dimensions of the superstring

Ist Teil von

• Nuclear physics. B, 1989-03, Vol.315 (2), p.528-540

Ort / Verlag

Amsterdam: Elsevier B.V

Erscheinungsjahr

1989

Quelle

Elsevier ScienceDirect Journals

Beschreibungen/Notizen

• We examine the possibility of constraining the dimensions M + 1 and N of the physical space-time and the internal space, respectively, of the D(= M + N + 1)-dimensional theory L=√− g ̂ ( 1 2 K ̂ −2 R ̂ + 1 2 Φ; AΦ; B g ̂ AB) , which is the field-theory limit of both the bosonic string and the superstring when higher-order terms K ̂ 2φ −4 (D−2) R ̂ 2 and K ̂ 2φ −8 (D−2) H ̂ ABC 2 can be ignored, where φ  exp( 1 2 √(D−2) K ̂ Φ) is the dilation. The Wheeler-De Witt equation for the wave function of the Universe ψ is derived for the topology R × S M × R N , where the space R N is to approximate a (Ricci-flat) Kähler space. By requiring that ψ remain finite at the origin (zero ( D − 1)-volume) and assuming that the eigenvalue of the dilaton energy-momentum tensor vanishes, we show that the metric initially possesses the “no-scale” form d s 2 = − n 2 d t 2 + a 2( t)d x 2 + a −2( t)d y 2, provided that ( M − N) 2 = M + N. This condition includes not only the cases D = 26 ( M = 10, N = 15) and D = 10 ( M = 3, N = 6), for which the dilaton beta function β φ vanishes (to lowest order in α′) in the bosonic string and the superstring, respectively, but also the case D = 5 ( M = 3, N = 1) corresponding to the original Kaluza-Klein theory. Since M = 3 for the physical space, then the superstring is allowed, while the bosonic string appears to be ruled out. The analysis was motivated by a preprint of Enqvist, Mohanty and Nanopoulos.