Dimensional reduction and the duality symmetry in the superstring theory

Journal Article · Mon Mar 30 00:00:00 EST 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X9200079X· OSTI ID:5397677

Pollock, M D ^[1]

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1. L.D. Landau Inst. for Theoretical Physics, Academy of Sciences of the USSR, Ulitsa Kosygina 2, Moscow 117940 (SU)

This paper reports on the D-dimensional superstring theory which is known to be invariant under the duality symmetry b {leftrightarrow} {alpha}{prime}/b, where b {equivalent to} e{sup {beta}} sq. root {alpha}{prime} is the constant radius of the N-dimensional internal space and {alpha}{prime} is the slope parameter, the (M + 1)-dimensional physical space-time being flat, where D = M + N + 1. It is shown, starting from the D-dimensional, vacuum Einstein theory, that this symmetry can be generalized to a curved space-time, with {beta}(t) = {minus}{alpha}(t) and t {leftrightarrow} t{sup 2}{sub 0}/t, where t is comoving time, but it will only be an isometry of the (conformally transformed) physical space if this is characterized by a single radius function e{sup {alpha}(t)}. This would explain the homogeneity, isotropy and flatness of the Universe. The dimensionalities are uniquely determined by the dimensional reduction to be D = 10, M = 3, N = 6. Further aspects of the duality symmetry are discussed and the notion of a negative dimension is introduced. For the closed type I superstring, density fluctuations sufficient to account for the presence of galaxies will be present, provided that G{mu} {approx lt} 10{sup {minus}6}, where G {equivalent to} M{sup {minus}2}{sub P} is the Newtonian gravitational constant, M{sub P} is the Planck mass and {mu} = {alpha}{prime}{sup 2}/2{pi}b{sup 6} is the effective mass per unit length of the string.

• OSTI ID: 5397677
• Journal Information: International Journal of Modern Physics A; (United States), Vol. 7:8; ISSN 0217-751X
• Country of Publication: United States
• Language: English

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