How to display a 4K picture through macbook retina HDMI connector

Not sure if this is supported:

From Apples support website:

http://support.apple.com/kb/SP653

• Intel HD Graphics 4000
• NVIDIA GeForce GT 650M with 1GB of GDDR5 memory and automatic graphics switching
• Dual display and video mirroring: Simultaneously supports full native resolution on the built-in display and up to 2560 by 1600 pixels on up to two external displays, at millions of colors

Thunderbolt digital video output

• Native Mini DisplayPort output
• DVI output using Mini DisplayPort to DVI Adapter (sold separately)
• VGA output using Mini DisplayPort to VGA Adapter (sold separately)
• Dual-link DVI output using Mini DisplayPort to Dual-Link DVI Adapter (sold separately)

rMBP (15-inch in particular) can output 4K through HDMI @ 24Hz, but only in Windows (Bootcamp)

Your TV is 1080p. How exactly do you expect it to do 4k? Not only that, but the HDMI output won't do it... as others have said, it's not a supported resolution for external display, but regardless, your TV cannot do it anyway.

Is that with the Apple Bootcamp drivers or nVidia drivers off that site?

So this seems to be a software issue rather than a hardware issue, meaning that it can be supported in the future.

I have the same TV you have 84" LG 84LM9600 UHD I've been able to use the MBPr HDMI output at 3840x2160@30hz but only via Windows 7 (Bootcamp) I cannot get it to work through OSX however which is a bit dissappointing. But its definetly an issue related to OSX since it works perfectly fine with Windows 7. The picture is jaw dropping needless to say. Especially when watching 4K youtube videos with res set to (Original). Make sure you use a HDMI 1.4a Highspeed cable as well.

Have you tried SwitchResX ?

Have you tried OSX 10.9 Mavericks DP?

Im about to find out in the very near future when my 84lm9600 arrives.