Gravity as the square of Yang-Mills?

TL;DR

This paper explores how gravitational theories can be understood as products of two Yang-Mills theories, revealing that their symmetries originate from the symmetries of the Yang-Mills factors, especially in the context of scattering amplitudes.

Contribution

It provides a concrete dictionary linking (super)gravity fields to the product of two (super) Yang-Mills theories, elucidating the origin of gravitational symmetries from Yang-Mills symmetries.

Findings

Gravity symmetries derived from Yang-Mills symmetries

Dictionary relating supergravity fields to Yang-Mills products

Implications for understanding gravitational theories via gauge theories

Abstract

In these lectures we review how the 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.