I went over to investigate, and saw that the cicada was being attacked by the biggest wasp I had ever seen. This thing was definitely larger than a hornet or a red wasp. The wasp had clearly hit the cicada in midair, and was clinging to it in a death grip, stinging it repeatedly. The cicada was buzzing its wings at first, but quickly fell still on it back.
I was surprised by what happened next. The wasp moved so so its head and the head of the now-dead cicada, clung to the belly of the cicada, and then took off into the air. I would never have guessed that the wasp could fly with so much weight; the cicada probably weighed five times as much as it did. It was like seeing a crow flying around with a large rabbit in its claws. The wasp buzzed around laboriously, slowly lifting off, almost hitting a car, and then went off into the bushes.
Maybe the wasp will eat the cicada, or maybe it will lay eggs in it. I do not know enough about insects to know what kind of wasp it was. I am guessing it was a solitary and not a social insect, and I saw a lot of bright red on it, but that is all I could say.