Updated models with AMD graphics options expected in early 2017.
2015 MacBook Air Can Drive 4K Displays at 60Hz
Apple's tech specs page for the new MacBook Air lists the notebook as capable of supporting one external display at up to 2,560×1,600 pixels, which clearly is not the case. Apple may be electing not to advertise 4K support for the new MacBook Air on purpose, however, as performance can still be somewhat laggy or jerky and the company has a shortlist of supported displays and configurations.
"Given that the Air is using one of Intel’s integrated GPUs, general OS X user interface performance isn’t too bad while driving the Air’s internal display alongside the 4K display. Dropped frames are clearly visible when entering into Full Screen mode or using Mission Control, and of course you’ll never want to try playing games or doing heavy 3D work at native resolution. But things are more than smooth enough for desktop use."The new Thunderbolt 2 port included on the refreshed MacBook Air and MacBook Pro is compatible with the DisplayPort 1.2 spec, meaning that Single-Stream Transport is possible using one cable. Meanwhile, 4K over HDMI remains restricted to a 24Hz refresh rate due to the limitations of the current 1.4 spec. Multi-Stream Transport should also be possible using DisplayPort 1.2, although the number of displays will be limited and performance will likely be impacted.
Update: Apple has now updated its tech specs page for the new MacBook Air to note that it supports external displays up to 3840 by 2160.