Abstract
The supersymmetry transformations under which the four-dimensional massless Dirac equation for a two-component, spin-1/2 fermion field ψ (the Weyl equation) remains invariant were obtained by Volkov and Akulov, who used the result to construct the action S = a-1 ∫ |W| d4x in terms of the energy-momentum tensor [Formula: see text], where Wij = δij + aTij and a is a constant. Here, we show, in the approximation [Formula: see text], that the terms linear, quadratic and quartic in Tij are contained in the bosonic sector of the dimensionally reduced, heterotic superstring action, including higher-derivative gravitational terms up to order ℛ4. By comparison of coefficients, we derive the value B r ≈ 3.5 for the radius squared of the internal space in units of the Regge slope parameter α′, slightly greater than the Hagedorn radius squared [Formula: see text]. The cubic terms are also discussed.
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