Whisk together the pomegranate juice, sugar, and balsamic vinegar in a saucepan over medium-high heat. Once the mixture comes to a boil, reduce heat to low, and simmer for about 35 minutes, or until reduced to a syrup. Whisk occasionally. It will be runny up until the end; then it will all of a sudden be a thick syrup. Remove from heat, and cover to keep warm.