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Non-Abelian gauged supergravities as double copies

Marco Chiodaroli, Murat Gunaydin, Henrik Johansson, Radu Roiban

Abstract

Scattering amplitudes have the potential to provide new insights to the study of supergravity theories with gauged R-symmetry and Minkowski vacua. Such gaugings break supersymmetry spontaneously, either partly or completely. In this paper, we develop a framework for double-copy constructions of Abelian and non-Abelian gaugings of N=8 supergravity with these properties. They are generally obtained as the double copy of a spontaneously-broken (possibly supersymmeric) gauge theory and a theory with explicitly-broken supersymmetry. We first identify purely-adjoint deformations of N=4 super-Yang-Mills theory that preserve the duality between color and kinematics. A combination of Higgsing and orbifolding yields the needed duality-satisfying gauge-theory factors with multiple matter representations. We present three explicit examples. Two are Cremmer-Scherk-Schwarz gaugings with unbroken N=6,4 supersymmetry and U(1) gauge group. The third has unbroken N=4 supersymmetry and SU(2)xU(1) gauge group. We also discuss examples in which the double-copy method gives theories with explicitly-broken supersymmetry.

Non-Abelian gauged supergravities as double copies

Abstract

Scattering amplitudes have the potential to provide new insights to the study of supergravity theories with gauged R-symmetry and Minkowski vacua. Such gaugings break supersymmetry spontaneously, either partly or completely. In this paper, we develop a framework for double-copy constructions of Abelian and non-Abelian gaugings of N=8 supergravity with these properties. They are generally obtained as the double copy of a spontaneously-broken (possibly supersymmeric) gauge theory and a theory with explicitly-broken supersymmetry. We first identify purely-adjoint deformations of N=4 super-Yang-Mills theory that preserve the duality between color and kinematics. A combination of Higgsing and orbifolding yields the needed duality-satisfying gauge-theory factors with multiple matter representations. We present three explicit examples. Two are Cremmer-Scherk-Schwarz gaugings with unbroken N=6,4 supersymmetry and U(1) gauge group. The third has unbroken N=4 supersymmetry and SU(2)xU(1) gauge group. We also discuss examples in which the double-copy method gives theories with explicitly-broken supersymmetry.

Paper Structure

This paper contains 23 sections, 105 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction and summary of results
  2. Color/kinematics duality with massive fermions and $\phi^3$ interactions
  3. Four-fermion amplitudes
  4. Two-fermion two-scalar amplitudes
  5. Four-scalar amplitudes
  6. Solution for general $F^{IJK}$ in $D$ dimensions
  7. Massive deformations of ${\cal N}=4$ SYM theory
  8. Solutions that uplift to $D>4$
  9. Solutions in $D=4$
  10. Relation between gauge-theory trilinear couplings and supergravity gauge group
  11. Gaugings of ${\cal N}=8$ supergravity with Minkowski vacua
  12. Examples
  13. Spontaneously-broken gaugings
  14. CSS gauging with ${\cal N}=6$ unbroken supersymmetry
  15. CSS gauging with ${\cal N}=4$ unbroken supersymmetry
  16. ...and 8 more sections

Figures (1)

  • Figure 1: Diagrams generically arising when a theory is taken on the Coulomb branch through assigning compact momenta. In some cases, the third diagram has vanishing color factor but is formally assigned a nonzero numerator factor. Mass flow follows the direction of the arrow and is conserved at each vertex.