You're probably thinking of The 13th Tribe by Arthur Koestler. He said that the Ashkenazi, who are the Jews who came from European countries except Spain, are descendants of the Khazars, who converted en masse in the Middle Ages. Apparently, the king of the Khazars had a priest, a rabbi, and an imam, and asked them which of the other two religions were better. The priest and the imam both said Judaism, so that's what he had the Khazars convert to.
The thing is, they weren't actually Slavic, but Turkic, and it was only really the upper class that converted. I don't doubt most Ashkenazi are part-Khazar. But it's a small part. Ashkenazi Cohens match Sephardic Cohens, and they look Slavic, not Turkish.
I don't think there's any reason the variety of Jews needs a mass conversion or a serious break in continuity to explain it. A small proportion of converts per generation can eventually have a huge impact.
Thanks, you're right.