Gluino Condensation in F-theory

Coupling of bilinears of gauginos on D-branes to anti-symmetric tensor fields can be deduced by comparing F-theory compactified to 8 dimensions with the heterotic string on $R^8\times T^2$. Application to SUSY breaking in F-theory triggered by gaugino condensation is discussed. Compactification to four dimensions with a warp factor is briefly discussed. In this case some 3-branes whose world-volume coincides with the open spacetime must be introduced, in addition to 7-branes.