Recent advances in generative AI have led to the development of techniques to generate visually realistic synthetic video. While a number of techniques have been developed to detect AI-generated synthetic images, in this paper we show that synthetic image detectors are unable to detect synthetic videos. We demonstrate that this is because synthetic video generators introduce substantially different traces than those left by image generators. Despite this, we show that synthetic video traces can be learned, and used to perform reliable synthetic video detection or generator source attribution even after H.264 re-compression. Furthermore, we demonstrate that while detecting videos from new generators through zero-shot transferability is challenging, accurate detection of videos from a new generator can be achieved through few-shot learning.