scholarly journals Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

2017 ◽  
Vol 2017 (7) ◽  
Author(s):  
Marco Chiodaroli ◽  
Murat Günaydin ◽  
Henrik Johansson ◽  
Radu Roiban
Keyword(s):  
Yang Mills ◽  
Explicit Formulae ◽  
Double Copy

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

scholarly journals Flat self-dual gravity

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Kirill Krasnov ◽  
Evgeny Skvortsov
Keyword(s):  
Light Cone ◽  
Space Time ◽  
Kinetic Term ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Covariant Action ◽  
Chiral Interaction ◽  
Double Copy

Abstract We construct a new covariant action for “flat” self-dual gravity in four space-time dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure.

scholarly journals Positive helicity Einstein-Yang-Mills amplitudes from the double copy method

2019 ◽  
Vol 99 (4) ◽  
Author(s):  
Josua Faller ◽  
Jan Plefka
Keyword(s):  
Yang Mills ◽  
Double Copy

scholarly journals Single particle operators and their correlators in free $$ \mathcal{N} $$ = 4 SYM

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
F. Aprile ◽  
J. M. Drummond ◽  
P. Heslop ◽  
H. Paul ◽  
F. Sanfilippo ◽  
...  
Keyword(s):  
Single Particle ◽  
Operator Product ◽  
Point Function ◽  
Superstring Theory ◽  
Yang Mills ◽  
Free Theory ◽  
Explicit Formulae ◽  
Orthogonality Theorem ◽  
Single Trace ◽  
Bps States

Abstract We consider a set of half-BPS operators in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which are appropriate for describing single-particle states of superstring theory on AdS5× S5. These single-particle operators are defined to have vanishing two-point functions with all multi-trace operators and therefore correspond to admixtures of single- and multi-traces. We find explicit formulae for all single-particle operators and for their two-point function normalisation. We show that single-particle U(N) operators belong to the SU(N) subspace, thus for length greater than one they are simply the SU(N) single-particle operators. Then, we point out that at large N, as the length of the operator increases, the single-particle operator naturally interpolates between the single-trace and the S3 giant graviton. At finite N, the multi-particle basis, obtained by taking products of the single-particle operators, gives a new basis for all half-BPS states, and this new basis naturally cuts off when the length of any of the single-particle operators exceeds the number of colours. From the two-point function orthogonality we prove a multipoint orthogonality theorem which implies vanishing of all near-extremal correlators. We then compute all maximally and next-to-maximally extremal free correlators, and we discuss features of the correlators when the extremality is lowered. Finally, we describe a half-BPS projection of the operator product expansion on the multi-particle basis which provides an alternative construction of four- and higher-point functions in the free theory.

scholarly journals Massive double copy in three spacetime dimensions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Mariana Carrillo González ◽  
Arshia Momeni ◽  
Justinas Rumbutis
Keyword(s):  
Scattering Amplitudes ◽  
Three Dimensional ◽  
Massive Gravity ◽  
Gauge Fields ◽  
Yang Mills ◽  
Double Copy ◽  
Topologically Massive Gravity

Abstract Recent explorations on how to construct a double copy of massive gauge fields have shown that, while any amplitude can be written in a form consistent with colour-kinematics duality, the double copy is generically unphysical. In this paper, we explore a new direction in which we can obtain a sensible double copy of massive gauge fields due to the special kinematics in three-dimensional spacetimes. To avoid the appearance of spurious poles at 5-points, we only require that the scattering amplitudes satisfy one BCJ relation. We show that the amplitudes of Topologically Massive Yang-Mills satisfy this relation and that their double copy at three, four, and five-points is Topologically Massive Gravity.

scholarly journals Effective action of dilaton gravity as the classical double copy of Yang-Mills theory

2019 ◽  
Vol 99 (2) ◽  
Author(s):  
Jan Plefka ◽  
Jan Steinhoff ◽  
Wadim Wormsbecher
Keyword(s):  
Effective Action ◽  
Dilaton Gravity ◽  
Yang Mills ◽  
Double Copy

scholarly journals On duality of color and kinematics in (A)dS momentum space

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Soner Albayrak ◽  
Savan Kharel ◽  
David Meltzer
Keyword(s):  
Wave Function ◽  
Analytic Continuation ◽  
Momentum Space ◽  
Spectral Representation ◽  
Flat Space ◽  
Tree Level ◽  
De Sitter ◽  
Yang Mills ◽  
The Universe ◽  
Double Copy

Abstract We explore color-kinematic duality for tree-level AdS/CFT correlators in momentum space. We start by studying the bi-adjoint scalar in AdS at tree-level as an illustrative example. We follow this by investigating two forms of color-kinematic duality in Yang-Mills theory, the first for the integrated correlator in AdS4 and the second for the integrand in general AdSd+1. For the integrated correlator, we find color-kinematics does not yield additional relations among n-point, color-ordered correlators. To study color-kinematics for the AdSd+1 Yang-Mills integrand, we use a spectral representation of the bulk-to-bulk propagator so that AdS diagrams are similar in structure to their flat space counterparts. Finally, we study color KLT relations for the integrated correlator and double-copy relations for the AdS integrand. We find that double-copy in AdS naturally relates the bi-adjoint theory in AdSd+3 to Yang-Mills in AdSd+1. We also find a double-copy relation at three-points between Yang-Mills in AdSd+1 and gravity in AdSd−1 and comment on the higher-point generalization. By analytic continuation, these results on AdS/CFT correlators can be translated into statements about the wave function of the universe in de Sitter.

scholarly journals Gravitational Dynamics—A Novel Shift in the Hamiltonian Paradigm

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 13
Author(s):  
Abhay Ashtekar ◽  
Madhavan Varadarajan
Keyword(s):  
General Relativity ◽  
Phase Space ◽  
Geometrical Interpretation ◽  
Lie Derivative ◽  
Hamiltonian Constraint ◽  
Yang Mills ◽  
Dirac Quantization ◽  
Perturbative Regime ◽  
Point Of Departure ◽  
Double Copy

It is well known that Einstein’s equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that time evolution of the gravitational field can be re-expressed as (a gauge covariant generalization of) the Lie derivative along a novel shift vector field in spatial directions. Thus, the canonical transformation generated by the Hamiltonian constraint acquires a geometrical interpretation on the Yang-Mills phase space, similar to that generated by the diffeomorphism constraint. In classical general relativity this geometrical interpretation significantly simplifies calculations and also illuminates the relation between dynamics in the ‘integrable’ (anti)self-dual sector and in the full theory. For quantum gravity, it provides a point of departure to complete the Dirac quantization program for general relativity in a more satisfactory fashion. This gauge theory perspective may also be helpful in extending the ‘double copy’ ideas relating the Einstein and Yang-Mills dynamics to a non-perturbative regime. Finally, the notion of generalized, gauge covariant Lie derivative may also be of interest to the mathematical physics community as it hints at some potentially rich structures that have not been explored.

scholarly journals New heavenly double copies

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Erick Chacón ◽  
Hugo García-Compeán ◽  
Andrés Luna ◽  
Ricardo Monteiro ◽  
Chris D. White
Keyword(s):  
Type Theory ◽  
Equation Of Motion ◽  
Field Theories ◽  
Classical Solutions ◽  
Related Field ◽  
Yang Mills ◽  
Hermitian Manifolds ◽  
Area Preserving ◽  
Double Copy ◽  
Special Case

Abstract The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, and related field theories. Previous work has shown that this has an explicit realisation in self-dual YM theory, where the equation of motion can be written in a form that maps directly to Plebański’s heavenly equation for self-dual gravity. The self-dual YM equation involves an area-preserving diffeomorphism algebra, two copies of which appear in the heavenly equation. In this paper, we show that this construction is a special case of a wider family of heavenly-type examples, by (i) performing Moyal deformations, and (ii) replacing the area-preserving diffeomorphisms with a less restricted algebra. As a result, we obtain a double-copy interpretation for hyper-Hermitian manifolds, extending the previously known hyper-Kähler case. We also introduce a double-Moyal deformation of the heavenly equation. The examples where the construction of Lax pairs is possible are manifestly consistent with Ward’s conjecture, and suggest that the classical integrability of the gravity-type theory may be guaranteed in general by the integrability of at least one of two gauge-theory-type single copies.

scholarly journals Efficient calculation of crossing symmetric BCJ tree numerators

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alex Edison ◽  
Fei Teng
Keyword(s):  
Quantum Gravity ◽  
Computational Efficiency ◽  
Parallel Study ◽  
Improved Method ◽  
Explicit Dependence ◽  
Yang Mills ◽  
Efficient Calculation ◽  
Crossing Symmetry ◽  
Scalar Theories ◽  
Double Copy

Abstract In this paper, we develop an improved method for directly calculating double-copy-compatible tree numerators in (super-)Yang-Mills and Yang-Mills-scalar theories. Our new scheme gets rid of any explicit dependence on reference orderings, restoring a form of crossing symmetry to the numerators. This in turn improves the computational efficiency of the algorithm, allowing us to go well beyond the number of external particles accessible with the reference order based methods. Motivated by a parallel study of one-loop BCJ numerators from forward limits, we explore the generalization to include a pair of fermions. To improve the accessibility of the new algorithm, we provide a Mathematica package that implements the numerator construction. The structure of the computation also provides for a straightforward introduction of minimally-coupled massive particles potentially useful for future computations in both classical and quantum gravity.

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