IS GRAVITINO CONDENSATION POSSIBLE?

Abstract

The condensation of fermion bilinears in the dimensionally-reduced, E 8× 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 λ 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 Helayël–Neto and Smith and by the present author, assuming the internal-space gravitinos [Formula: see text] to condense close to the compactification scale M c ~M P /10. Here, by including the four-fermion terms in the Lagrangian density ℒ, we point out that the observable-sector gravitinos ψi and gauginos g typically have comparable, but not identical, masses m3/2~mg~M c as a result of this process. Hence, such condensation is only permitted either at the much lower scale [Formula: see text] (as for the hidden-sector gaugino condensation), so that [Formula: see text], the upper limit on mg ensuring that the Higgs doublets are sufficiently light or, more plausibly, by setting 1 TeV ~mg≪m3/2~M c , which requires a constraint on the condensate parameters. If the three-index field [Formula: see text] also condenses, then the vacuum expectation value of the dimensionless combination [Formula: see text] of the dilaton A r and modulus B r is fixed at a scale ~1, thus yielding the Kähler potential K and hence m3/2~M c Since B r is determined from supersymmetry, this mechanism determines A r .