Is gravitino condensation possible?

摘要

The condensation of fermion bilinears in the dimensionally-reduced, E-8 x E-8' heterotic superstring theory often refers to the E-8' hidden-sector gauginos, but in principle condensation may also occur in the compactified internal space, for example of the gravitino and the spin-1/2 Majorana-Weyl field lambda of eleven-dimensional supergravity. This possibility, raised by Duff and Orzalesi as a method of spontaneous compactification that maintains vanishing vacuum energy (cosmological constant), was subsequently considered in the context of the heterotic superstring theory by Helayel-Neto and Smith and by the present author, assuming the internal-space gravitinos psi(mu) to condense close to the compactification scale M-c similar to M-p/10. Here, by including the four-fermion terms in the Lagrangian density L, we point out that the observable-sector gravitinos psi(i) and gauginos g typically have comparable, but not identical, masses m(3/2) similar to m(g) similar to M-c as a result of this process. Hence, such condensation is only permitted either at the much lower scale (&ULambda;) over tilde similar to 5 x 10(13) GeV (as for the hidden-sector gaugino condensation), so that m(3/2) similar to m(g) similar to kappa(2)(&ULambda;) over tilde (3) similar to 1 TeV, the upper limit on m(g) ensuring that the Higgs doublets are sufficiently light or, more plausibly, by setting 1 TeV similar to m(g) much less than m(3/2) similar to M-c, which requires a constraint on the condensate parameters. If the three-index field H-munuxi also condenses, then the vacuum expectation value of the dimensionless combination A(r)B(r)(3) of the dilaton A(r) and modulus B-r is fixed at a scale similar to 1, thus yielding the Kahler potential K and hence m(3/2) similar to M-c. Since B-r is determined from supersymmetry, this mechanism determines A(r) .