Abstract
The heterotic superstring theory, after reduction to four dimensions, is known to contain two axions, found by Witten, and studied further by Choi and Kim. One combination of these can be identified with the axion of Peccei and Quinn, whose energy scale is then given by the formula [Formula: see text], where [Formula: see text] is the ratio of the two separate energy scales, g s is the strong-interaction coupling constant and M P ≡G−1/2 is the Planck mass, G being the Newton gravitational constant. This agrees with the result obtained by Choi and Kim, apart from a factor of [Formula: see text], which is explained. For a supersymmetric theory, Steinhardt and Turner have shown, developing an idea by Weinberg, that the upper limit on this parameter, corresponding to a closed Universe today, is f a ≲1013ζ9/11≈4×1016 GeV , where ζ≲3×104 is the entropy enhancement accompanying the decay of a supersymmetric particle, presumed to be the gravitino of mass M g ≈104 GeV . These two calculations of f a differ only by a factor of 15 (agreement is obtained for M g ≈106−107 GeV ), suggesting that axions may constitute the dark matter of the Universe. Some further aspects of superstring axions are discussed, including their rôle in the formation of wormholes.
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