Yang-Mills Origin of Gravitational Symmetries

Abstract

By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincaré. As a concrete example we focus on the new-minimal (12+12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4 + 4, NL = 1) and (3 + 0, NR = 0).PACS numbers: 11.25.-w Keywords: super-Yang-Mills, supergravity, local symmetries In Einstein's general theory of relativity the requirement that the laws of physics be the same to all observers is embodied in the principle of general covariance: the equations must be invariant under arbitrary coordinate transformations. Fermions require in addition local Lorentz invariance and many models of interest also incorporate local supersymmetry and local p-form gauge invariance. The purpose of this paper is to derive, in linearised approximation, all these gravitational symmetries starting from those of flat-space Yang-Mills, namely local gauge invariance and global (super)-Poincaré.Early attempts to derive gravity from Yang-Mills were based on gauging spacetime symmetries such as Lorentz, Poincaré or de Sitter [1][2][3][4][5]. More recently, the AdS/CFT correspondence has provided a different link between gravity and gauge theories [6][7][8]. However, our approach will differ from both in important respects. We appeal to the idea of "Gravity as the square of Yang-Mills" by tensoring left and right multiplets with arbitrary nonAbelian gauge groups G L and G R . Squaring Yang-Mills is a recurring theme in attempts to understand the quantum theory of gravity and appears in several different forms: Closed states from products of open states and KLT relations in string theory [9][10][11] 3,4,5,6,8,9,10,12,16. This 4×4 square in D = 3 is the base of a "magic pyramid" with a 3 × 3 square in D = 4, a 2 × 2 square in D = 6 and Type II supergravity at the apex in D = 10 [28]. In this paper we focus instead on the Yang-Mills origin of the local gravitational symmetries of general covariance, local Lorentz invariance, local supersymmetry and p-form gauge invariance acting on the classical fields.Although much of the squaring literature invokes taking a product of left and right Yang-MiIls fields

Non-Abelian gauged supergravities as double copies

“…Effective non-gravitational theories for which a double-copy construction is known include the Dirac-Born-Infeld and the special Galileon theories, as well as the nonlinear sigma model [38,39,40,41,42,43,44]. Double-copy structures have also been identified for various string-theory amplitudes, [45,46,47,48,49,50,51,52,53], within the Cachazo-He-Yuan formalism [54,55,56,57,58], in the context of ambitwistor string theories [59], and at the level of linearized supermultiplets [60,61,62,63,64].…”

Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string

“…[20][21][22][23][24] for explicit solution relationships, and refs. [25][26][27][28][29][30] for considerations of classical symmetries and duality-groups, as well as references therein.…”

Multi-centered N = 2 $$ \mathcal{N}=2 $$ BPS black holes: a double copy description

“…We use this dictionary to write down the explicit double copy expression for general multi-centered dyonic BPS black holes in these theories, in the weak-field approximation. This dictionary makes use of a convolution ⋆ [15], by means of which one expresses gravitational field configurations ϕ G on the supergravity side in terms of field theory configurations ϕ andφ, ϕ G = ϕ ⋆φ .…”