George Musser in Scientific American:
Vasiliev theory (for sake of a pithy name, physicists drop Fradkin’s name) takes to extremes the basic idea of modern physics: that the world around us consists of fields—the electrical and magnetic fields and a handful of others that represent the known forces of nature and types of matter. Vasiliev theory posits an infinite number of fields. They come in progressively more complicated varieties described by the quantum-mechanical property of spin.
Spin is perhaps best thought of as the degree of rotational symmetry. The electromagnetic field along with its associated particle, the photon, has spin-1. If you rotate it 360 degrees, it looks the same as before. The gravitational field along with its associated particle, the graviton, has spin-2: you need to rotate it only 180 degrees. The known particles of matter, such as the electron, have spin-1/2: you need to rotate them 720 degrees before they return to their original appearance—a counterintuititive feature that turns out to explain why these particles resist bunching, giving matter its integrity. The Higgs field has spin-0 and looks the same no matter how you rotate it.
In Vasiliev theory, there are also spin-5/2, spin-3, spin-7/2, spin-4, all the way up. Physicists used to assume that was impossible. These higher-spin fields, being more symmetrical, would imply new laws of nature analogous to the conservation of energy, and no two objects could ever interact without breaking one of those laws. The workings of nature would seize up like an overregulated economy. At first glance, string theory, the leading candidate for a fully unified theory of nature, runs afoul of this principle. Like a plucked guitar string, an elementary quantum string has an infinity of higher harmonics, which correspond to higher-spin fields. But those harmonics come with an energy cost, which keeps them inert.
Vasiliev and Frakin showed that the above reasoning applies only when gravity is insignificant and spacetime is not curved. In curved spacetimes, higher-spin fields can exist after all. Maybe overregulation isn’t such a bogeyman after all.