Gravity as the square of Yang-Mills?

Abstract

In these lectures we review how symmetries of gravitational theories may be regarded as originating from those of 'Yang–Mills squared'. We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang–Mills theories, particularly in the context of scattering amplitudes. We then introduce a concrete dictionary for the covariant fields of (super)gravity in terms of the product of two (super) Yang–Mills theories. The dictionary implies that the symmetries of each (super) Yang–Mills factor generate the symmetries of the corresponding (super)gravity theory: general covariance, p-form gauge invariance, local Lorentz invariance, local supersymmetry, R-symmetry and U-duality.