A vertex operator algebra construction of the colour-kinematics dual numerator

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)× U (1) gauge group. We also discuss examples in which the double-copy method gives theories with explicitly-broken supersymmetry.

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Non-Abelian gauged supergravities as double copies

Chiodaroli

Günaydın

Johansson

et al. 2019

“…It is curious to note that the objects that the kinematic Lie algebra should compute, the kinematic BCJ numerators, are under better control than the algebra itself. Numerators that manifest the color-kinematics duality have been constructed at any multiplicity for tree-level amplitudes in pure Yang-Mills theory [20][21][22][23][24][25][26][27]. For supersymmetric Yang-Mills theory, it has been observed that a recursive construction similar to Berends-Giele recursion [28] can be used to generate BCJ numerators after using appropriate non-linear gauge transformations [23].…”

Section: Introductionmentioning

confidence: 99%

“…[70]), that yields local Yang-Mills numerators from a closed algebra. For non-local numerators there exists an algebraic construction using string vertex operators [27].…”

Section: Introductionmentioning

confidence: 99%

On the kinematic algebra for BCJ numerators beyond the MHV sector

Chen

Johansson

Teng

et al. 2019

106

The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggest the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain O (ε i ·ε j ) 2 terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents controls the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory.1 Cubic interactions are obtained by the replacement Tr([A µ , A ν ] 2 ) → − 1 2 (B µν ) 2 +Tr([A µ , A ν ]B µν ).

“…This technique, together with unitarity methods [34], has allowed for studies of the ultraviolet behaviour of supergravity theories. At tree level, the colour-kinematics duality is well-established, even if its algebraic origin remains to be satisfactorily explained; see, for instance, the constructions [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. The status of the loop-level conjecture is unclear, however.…”

mentioning

confidence: 99%

Two-loop scattering amplitudes: double-forward limit and colour-kinematics duality

Geyer

Monteiro

Stark-Muchão

2019

We propose new formulae for the two-loop n-point D-dimensional integrands of scattering amplitudes in Yang-Mills theory and gravity. The loop integrands are written as a double-forward limit of tree-level trivalent diagrams, and are inferred from the formalism of the two-loop scattering equations. We discuss the relationship between the formulae for non-supersymmetric theories and the Neveu-Schwarz sector of the formulae for maximally supersymmetric theories, which can be derived from ambitwistor strings. An important property of the loop integrands is that they are expressed in a representation that includes linear-type propagators. This representation exhibits a loop-level version of the colour-kinematics duality, which follows directly from tree level via the double-forward limit. arXiv:1908.05221v1 [hep-th] Contents 6 Conclusion 32 A Two-loop partition functions and propagators on the Riemann sphere 33 A.1 Two-loop partition functions 33 A.2 Two-loop propagators 341 IntroductionWorldsheet techniques inspired by string theory offer an alternative to the Feynman diagram approach for calculating scattering amplitudes in quantum field theory, in particular for theories of massless particles. This broad programme has seen remarkable advances in recent years. Our aims are to extend the lessons learned at tree level and one loop to two-loop amplitudes, and to interpret previous two-loop results for maximally supersymmetric theories in a more general context, allowing for reduced or no supersymmetry. Even though we will motivate our proposal for two-loop amplitudes from the insights of this 'stringy' approach, the proposal itself will not be written in a worldsheet language. It will instead be written in a (non-Feynman) diagrammatic language, whereby the two-loop integrands are suitably defined double-forward limits of tree-level amplitudes. The worldsheet techniques that inspire our work originated in Witten's twistor string [1] describing four-dimensional super-Yang-Mills theory, and in the corresponding 'connected prescription' to compute scattering amplitudes [2]. In this approach, tree-level scattering amplitudes for n massless particles are computed as integrals over the moduli space of punctured Riemann spheres, M 0,n . The -1 -modern version of these advances, applicable to theories of massless particles in any number of dimensions, was developed by Cachazo, He and Yuan (CHY) [3][4][5], who discovered the general type of formulae, and by Mason and Skinner [6], who constructed the associated type of worldsheet model; the ambitwistor string. For a variety of interesting theories in this framework, see e.g. [7,8]. The ambitwistor string models reproducing Yang-Mills and gravity amplitudes are supersymmetric, but the extraction of amplitudes in non-supersymmetric theories is possible even at loop level, as we shall discuss. For a comparison of the bosonic and supersymmetric ambitwistor strings, see [9,10]. For recent work on moduli-space formulae tuned to a specific number of spacetime dimensions using the spinor...