What was found
AT 39,000 FEET WHILE IN CRUISE WE HEARD A LOUD BANG. AT THAT TIME, CABIN ALTITUDE BEGAN RISING 750' PER MINUTE. WE WERE AT AROUND 9.0 PSI DIFFERENTIAL AROUND 6000 FEET CABIN ALT. WITHIN MINUTES WE KEPT CLIMBING TO 14000' CABIN ALTITUDE. EMERGENCY DESCENT AND DIVERSION RESULTED FROM THIS ISSUE. THE AMBER AND RED CABIN PRESSURIZATION CAS MSGS WERE DISPLAYED. COMPLIED WITH DETAIL INSPECTION OF BOTH LH AND RH SIDE DUCTS. FOUND RH DUCT TO BE BUSTED. REMOVED RH C0NDID0NED AIR DUCT AND INSTALLED CUSTOMER PROVIDED NEW AIR DUCT PER AMM 21-22-05. OPS AND LEAK CHECK GOOD AT THIS TIME