While working on “The Dark Queens: The Bloody Rivalry that Forged the Medieval World,” Shelley Puhak stumbled across a connection between her subjects and Shakespeare. Her book is a dual biography of Brunhild and Fredegund, two queens who, as long-term regents for their underage male relatives, ruled over most of sixth-century Western Europe. Fredegund was born a slave; Brunhild was a Visigoth princess. Despite their vastly different backgrounds, they ended up as sisters-in-law and political rivals who negotiated with emperors and popes, revitalized cities, revamped tax policy, and conducted a decades-long civil war—against each other. Echoes of one conflict in that war, the 593 Battle of Droizy, have been preserved in Macbeth’s final act, when Birnam Wood arrives at Dunsinane.