It’s not likely down to indexing which, as wuub points out, should stop after a short time. Other thoughts:
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Plugins could be responsible. Try disabling all your plugins temporarily to see if that fixes the problem. If it does, bring them in one by one until you find the offending plugin.
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If you’re using a laptop with particularly aggressive power saving. Say your quad-core puppy runs at 3Ghz clock, but an aggressive power saving scheme downclocks the system to 400hz, or turns off some of the cores, or both - when it deems the system to be “idle”. In that case, processes using a tiny bit of CPU will actually look like they’re using a lot more, since 6% of 400hz is <1% of 3Ghz. Try putting your laptop into max performance profile and see what the CPU use is then.
Personally I don’t see sublime doing much of anything when idle. Rarely do I see anything other than 0 on the sublime process. If you’re editing particularly large files, or editing across a network, this could also have a minor impact on CPU as sublime will “poll” files and/or swap stuff in and out.
If you’ve no plugins enabled and no files loaded and still seeing 6%, well, you got me… Perhaps there’s something Mac-specific going on here, as I use Sublime only on Linux and Windows.