Gravity as the square of Yang-Mills?

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.

Typos fixed. 26 pages, 6 figs. Based on lectures delivered by M. J. Duff at the Richard Arnowitt Symposium. Published in the Focus Issue on gravity, supergravity and fundamental physics: the Richard Arnowitt Symposium. Chosen as Physica Scripta's Paper of the Week 01/12/2015

References in corpus (12)

• New Relations for Gauge-Theory Amplitudes
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• E7(7) constraints on counterterms in N=8 supergravity
• Yang-Mills origin of gravitational symmetries
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Black Holes, Qubits and Octonions
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• A magic square from Yang-Mills squared
• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations

Cited by in corpus (38)

• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• The Kerr-Schild double copy in curved spacetime
• Scattering on plane waves and the double copy
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Gravity as Gauge Theory Squared: A Ghost Story
• A Twistorial Foundation for the Classical Double Copy
• S-duality and the Double Copy
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• Double Copy from Homotopy Algebras
• Topology and Wilson lines: global aspects of the double copy
• Extended solutions for the biadjoint scalar field
• Are all supergravity theories Yang-Mills squared?
• A double copy for asymptotic symmetries in the self-dual sector
• Twin Supergravities from Yang-Mills Squared
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Ehlers as EM duality in the double copy
• Weyl doubling
• Monopoles, shockwaves and the classical double copy
• Biadjoint wires
• New heavenly double copies
• Massive Gravity from Double Copy
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Radiation of scalar modes and the classical double copy
• Gauge $\times$ Gauge on Spheres
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Anti-de Sitter particles and manifest (super)isometries
• The Conformal BMS Group
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• Spin-four N=7 W-Supergravity: S-fold and Double Copy Construction
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• On symmetries and dynamics of exotic supermultiplets
• The Weyl double copy from twistor space
• Cotton Double Copy for Gravitational Waves
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday