On the supersymmetric dirac equation and the heterotic superstring theory

摘要

The supersymmetry transformations under which the four-dimensional massless Dirac equation for a two-component, spin-1/2 fermion field phi (the Weyl equation) remains invariant were obtained by Volkov and Akulov, who used the result to construct the action S = a(-1) f Wd(4)x in terms of the energy-momentum tensor T-ij = 1/2iphi + sigma((i)(&PARTIAL;) over left right arrow (j))phi, where W-ij = delta(ij) + T-ij and a is a constant. Here, we show, in the approximation T-ij approximate to (R-ij - 1/2g(ij)R)/kappa(2), that the terms linear, quadratic and quartic in T-ij are contained in the bosonic sector of the dimensionally reduced, heterotic superstring action, including higher-derivative gravitational terms up to order R-4. By comparison of coefficients, we derive the value B-r approximate to 3.5 for the radius squared of the internal space in. units of the Regge slope parameter alpha', slightly greater than the Hagedorn radius squared B-r((H)) = 2.914. The cubic terms are also discussed. [References: 34]