Why do super sonic fighter jets have narrow waist?
It is likely due to application of the Area rule, which helps to reduce drag due to shock waves in transonic and supersonic flight.

It basically is an attempt to keep the cross-sectional area of the craft from varying rapidly as you move along the length.  So at a point where the wings area is increasing a lot, the area of the fuselage may be reduced to compensate.  

This reduction of area is mainly intended when these airplanes fly at transonic speeds (0.8-1.2) but not when flying at supersonice speeds where a front shock wave is created.