[Paper Review] Non-Abelian gauged supergravities as double copies

Marco Chiodaroli, Murat Günaydin+2 more|arXiv (Cornell University)|Dec 26, 2018

Black Holes and Theoretical Physics71 references4 citations

TL;DR

This paper introduces a double-copy framework to construct non-Abelian gauged ${\cal N}=8$ supergravities with Minkowski vacua by combining a spontaneously-broken gauge theory and a theory with explicitly-broken supersymmetry. It identifies massive deformations of ${\cal N}=4$ super-Yang-Mills that preserve color-kinematics duality, enabling the construction of three explicit examples: two Cremmer-Scherk-Schwarz gaugings with unbroken ${\cal N}=6$ and ${\cal N}=4$ supersymmetry, and one with $SU(2)\times U(1)$ gauge group and ${\cal N}=4$ supersymmetry, all arising via double-copy mechanisms.

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.

Motivation & Objective

• To develop a double-copy framework for constructing non-Abelian gauged supergravities with Minkowski vacua and spontaneously broken supersymmetry.
• To identify massive deformations of ${\cal N}=4$ super-Yang-Mills that preserve color-kinematics duality.
• To construct explicit examples of gauged supergravities with unbroken ${\cal N}=6$, ${\cal N}=4$, and $SU(2)\times U(1)$ gauge symmetry via double-copy methods.
• To extend the double-copy program to theories with both spontaneously and explicitly broken supersymmetry.

Proposed method

• Utilize color-kinematics duality by constructing gauge-theory amplitudes where numerator factors satisfy the same algebraic relations as color factors.
• Apply Higgsing and orbifolding to deform ${\cal N}=4$ super-Yang-Mills into theories with multiple matter representations and massive fermions while preserving duality.
• Construct the double copy by replacing color factors with kinematic numerators from a second gauge theory, yielding gravitational amplitudes.
• Employ the embedding tensor formalism to identify consistent gaugings of ${\cal N}=8$ supergravity with Minkowski vacua.
• Use spinor-helicity and gamma matrix conventions in $D=4$ and $D=10$ to compute amplitudes and verify duality conditions.
• Derive Feynman rules for massive fermions and scalar-gluon vertices to compute scattering amplitudes in the deformed gauge theories.

Experimental results

Research questions

• RQ1 Can non-Abelian gauged ${\cal N}=8$ supergravities with Minkowski vacua be constructed via double-copy methods?
• RQ2 Which deformations of ${\cal N}=4$ super-Yang-Mills preserve color-kinematics duality while introducing mass terms and multiple matter representations?
• RQ3 How can double-copy constructions be extended to include theories with both spontaneously and explicitly broken supersymmetry?
• RQ4 What are the explicit gauge groups and unbroken supersymmetry algebras realized in double-copy-based gauged supergravities?
• RQ5 Can the double-copy framework reproduce known Cremmer-Scherk-Schwarz gaugings with ${\cal N}=6$ and ${\cal N}=4$ unbroken supersymmetry?

Key findings

• Three explicit examples of non-Abelian gauged ${\cal N}=8$ supergravities with Minkowski vacua are constructed via double-copy methods, including two Cremmer-Scherk-Schwarz gaugings with unbroken ${\cal N}=6$ and ${\cal N}=4$ supersymmetry.
• The $SU(2)\times U(1)$ gauging with unbroken ${\cal N}=4$ supersymmetry is realized through a double-copy construction involving a massive, duality-satisfying gauge theory.
• Massive deformations of ${\cal N}=4$ super-Yang-Mills that preserve color-kinematics duality are identified via Higgsing and orbifolding, enabling consistent double-copy constructions.
• The framework successfully generates supergravities with both spontaneously broken and explicitly broken supersymmetry, demonstrating the versatility of the double-copy approach.
• The double-copy construction reproduces known embedding tensor structures for $SO(8)$-like gaugings in ${\cal N}=8$ supergravity, validating the method.
• Feynman rules for massive fermions and trilinear couplings are derived, ensuring consistency in amplitude computations under the duality framework.