Delta dropped their sponsorship of the Falcons back in 2009.

https://blogs.wsj.com/middleseat/200...to-yanks-mets/

Air Tran (pre-merger with WN) was the "official airline" of the Falcons; but then it turned out that the Falcons used Delta charters on road trips.

Atlanta Falcons Do Not Fly on AirTran, Their Official Airline - AirlineReporter.com

Delta has major advertising links with the Braves and the Hawks; I'm guessing that since these two franchises, when put together, play multiple times per week year round, spending money with the Falcons constituted diminishing returns.

I'm curious whether Delta will ever obtain the naming rights to another stadium or arena, after they had to drop their sponsorship of the Utah Jazz arena (the former "Delta Center") when they filed for Chapter 11 bankruptcy a decade ago. They probably passed on or got outbid for the naming rights to the new Braves stadium, SunTrust Park.

Outside of markets such as Atlanta and New York, Delta got involved as "official airline" of a number of university athletic departments, including Notre Dame. They also are the airline sponsor of the Washington Nationals, even though three other airlines have hubs in the DC area (IAD-United; DCA-American; BWI-Southwest).