The resolution isn't quite good enough for me to be sure....
but it looks like adult and juvenile aphids, which are exceptionally common on peppers.
I deal with them every year when I overwinter peppers. I use Ladybugs to deal with them,
but you could also try manually removing them, spraying them off, using Neem oil, or using
one of many insecticidal soaps on the market. If you use an oil or a soap, rinse the plant
before it sees light again.

Ladybugs (or, rather, Ladybug larvae) are the best method.

Josh

Thanks for your suggestion, Josh. I initially thought they were a species of aphids too, but the good news is that I found all of them dead the day after I found them swarming under my grow light. Others have suggested that they might have been fungus gnats or something similar. I'm really glad they weren't aphids because that would have required a much more labor-intensive treatment. Glad it worked out on its own!