Line 11 would directly link the Airport with Downtown San Jose! It runs from Diridon Station, past the Convention Center, down 1st Street, then onto Highway 87 and does a full loop of SJC hitting both terminals (see the map below). Needless to say, Line 11 would be extremely convenient for Downtown residents and visitors alike. The line would run every 30 minutes from 5am to 11pm, seven days a week. Service will hopefully begin in October of this year.
Line 56 runs between the Component Lightrail Station in North San Jose and the Sunnyvale Caltrain Station (via Arques/Scott/Central Expressway). This would improve access and transit options for all of the companies in the Golden Triangle, including the burgeoning Renovation Row area.
For all of the details, head over to this VTA page.