scholarly journals The Weyl double copy from twistor space

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Erick Chacón ◽  
Silvia Nagy ◽  
Chris D. White
Keyword(s):  
Exact Solutions ◽  
Twistor Space ◽  
Current Form ◽  
New Formalism ◽  
Petrov Types ◽  
Gravity Theories ◽  
Double Copy

Abstract The Weyl double copy is a procedure for relating exact solutions in biadjoint scalar, gauge and gravity theories, and relates fields in spacetime directly. Where this procedure comes from, and how general it is, have until recently remained mysterious. In this paper, we show how the current form and scope of the Weyl double copy can be derived from a certain procedure in twistor space. The new formalism shows that the Weyl double copy is more general than previously thought, applying in particular to gravity solutions with arbitrary Petrov types. We comment on how to obtain anti-self-dual as well as self-dual fields, and clarify some conceptual issues in the twistor approach.

scholarly journals Lie polynomials and a twistorial correspondence for amplitudes

2021 ◽  
Vol 111 (6) ◽  
Author(s):  
Hadleigh Frost ◽  
Lionel Mason
Keyword(s):  
Moduli Space ◽  
Twistor Space ◽  
Riemann Sphere ◽  
Momentum Conservation ◽  
Mathematical Framework ◽  
Penrose Transform ◽  
Invariant Description ◽  
Logarithmic Singularities ◽  
Gravity Theories ◽  
Double Copy

AbstractWe review Lie polynomials as a mathematical framework that underpins the structure of the so-called double copy relationship between gauge and gravity theories (and a network of other theories besides). We explain how Lie polynomials naturally arise in the geometry and cohomology of $$\mathcal {M}_{0,n}$$ M 0 , n , the moduli space of n points on the Riemann sphere up to Mobiüs transformation. We introduce a twistorial correspondence between the cotangent bundle $$T^*_D\mathcal {M}_{0,n}$$ T D ∗ M 0 , n , the bundle of forms with logarithmic singularities on the divisor D as the twistor space, and $$\mathcal {K}_n$$ K n the space of momentum invariants of n massless particles subject to momentum conservation as the analogue of space–time. This gives a natural framework for Cachazo He and Yuan (CHY) and ambitwistor-string formulae for scattering amplitudes of gauge and gravity theories as being the corresponding Penrose transform. In particular, we show that it gives a natural correspondence between CHY half-integrands and scattering forms, certain $$n-3$$ n - 3 -forms on $$\mathcal {K}_n$$ K n , introduced by Arkani-Hamed, Bai, He and Yan (ABHY). We also give a generalization and more invariant description of the associahedral $$n-3$$ n - 3 -planes in $$\mathcal {K}_n$$ K n introduced by ABHY.

scholarly journals Higher-derivative heterotic Double Field Theory and classical double copy

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Eric Lescano ◽  
Jesús A. Rodríguez
Keyword(s):  
Field Theory ◽  
Exact Solutions ◽  
Maxwell Equations ◽  
Action Principle ◽  
Low Energy ◽  
Gauge Fields ◽  
Metric Tensor ◽  
Higher Derivative ◽  
Double Field Theory ◽  
Double Copy

Abstract The generalized Kerr-Schild ansatz (GKSA) is a powerful tool for constructing exact solutions in Double Field Theory (DFT). In this paper we focus in the heterotic formulation of DFT, considering up to four-derivative terms in the action principle, while the field content is perturbed by the GKSA. We study the inclusion of the generalized version of the Green-Schwarz mechanism to this setup, in order to reproduce the low energy effective heterotic supergravity upon parametrization. This formalism reproduces higher-derivative heterotic background solutions where the metric tensor and Kalb-Ramond field are perturbed by a pair of null vectors. Next we study higher-derivative contributions to the classical double copy structure. After a suitable identification of the null vectors with a pair of U(1) gauge fields, the dynamics is given by a pair of Maxwell equations plus higher derivative corrections in agreement with the KLT relation.

scholarly journals Noether symmetries as a geometric criterion to select theories of gravity

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1840007 ◽  
Author(s):  
Konstantinos F. Dialektopoulos ◽  
Salvatore Capozziello
Keyword(s):  
Exact Solutions ◽  
Cosmological Models ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Field Equations ◽  
Geometric Criterion ◽  
Symmetry Approach ◽  
Theories Of Gravity ◽  
Gravity Theories

We review the Noether Symmetry Approach as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories. The method allows to find out exact solutions, but also to constrain arbitrary functions in the action. Specific cosmological models are taken into account.

scholarly journals The Newman-Penrose map and the classical double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Gilly Elor ◽  
Kara Farnsworth ◽  
Michael L. Graesser ◽  
Gabriel Herczeg
Keyword(s):  
Exact Solutions ◽  
Gauge Theories ◽  
Flat Space ◽  
Classical Setting ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Space Vacuum ◽  
Double Copy ◽  
Systematic Framework ◽  
Made In

Abstract Gauge-gravity duality is arguably our best hope for understanding quantum gravity. Considerable progress has been made in relating scattering amplitudes in certain gravity theories to those in gauge theories — a correspondence dubbed the double copy. Recently, double copies have also been realized in a classical setting, as maps between exact solutions of gauge theories and gravity. We present here a novel map between a certain class of real, exact solutions of Einstein’s equations and self-dual solutions of the flat-space vacuum Maxwell equations. This map, which we call the Newman-Penrose map, is well-defined even for non-vacuum, non-stationary spacetimes, providing a systematic framework for exploring gravity solutions in the context of the double copy that have not been previously studied in this setting. To illustrate this, we present here the Newman- Penrose map for the Schwarzschild and Kerr black holes, and Kinnersley’s photon rocket.

scholarly journals A NOTE ON TWO-DIMENSIONAL DILATON GRAVITY WITH NON-SMOOTH POTENTIALS

2005 ◽  
Vol 20 (14) ◽  
pp. 1057-1064
Author(s):  
CHRISTIAN G. BÖHMER ◽  
PIOTR BRONOWSKI
Keyword(s):  
Exact Solutions ◽  
Brane World ◽  
Two Dimensional ◽  
Dilaton Gravity ◽  
First Order ◽  
Recent Interest ◽  
Different Types ◽  
Gravity Theories

Recent interest in brane world models motivates the investigation of generic first-order dilaton gravity actions, with potentials having some non-smoothness. We consider two different types of δ-like contributions in the action and analyse their effects on the solutions. Furthermore a second source of non-smoothness arises due to the remaining ambiguities in the solutions in the separated smooth patches, after fixing all other constants by matching and asymptotic conditions. If moreover staticity is assumed, we explicitly construct exact solutions. With the methods described, for example models with point like sources or brane world models (where the second source of non-smoothness becomes crucial), can now be treated as non-smooth dilaton gravity theories.

scholarly journals Generic off-diagonal solutions and solitonic hierarchies in (modified) gravity

2015 ◽  
Vol 30 (19) ◽  
pp. 1550090 ◽  
Author(s):  
Sergiu I. Vacaru
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Modified Gravity ◽  
Field Equations ◽  
Physical Data ◽  
Modified Gravity Theories ◽  
De Vries ◽  
Einstein Spaces ◽  
Curve Flows ◽  
Gravity Theories

We have summarized our recent results on encoding exact solutions of field equations in Einstein and modified gravity theories into solitonic hierarchies derived for nonholonomic curve flows with associated bi-Hamilton structure. We argue that there is a canonical distinguished connection for which the fundamental geometric/physical equations decouple in general form. This allows us to construct very general classes of generic off-diagonal solutions determined by corresponding types of generating and integration functions depending on all (spacetime) coordinates. If the integral varieties are constrained to zero torsion configurations, we can extract solutions for the general relativity (GR) theory. We conclude that the geometric and physical data for various classes of effective/modified Einstein spaces can be encoded into multi-component versions of the sine-Gordon, or modified Korteweg–de Vries equations.

scholarly journals Note on the asymptotic structure of Kerr-Schild form

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Pujian Mao ◽  
Weicheng Zhao
Keyword(s):  
Exact Solutions ◽  
Solution Space ◽  
Null Infinity ◽  
Asymptotic Structure ◽  
Asymptotically Flat ◽  
In Series ◽  
Pp Wave ◽  
Double Copy ◽  
Loss Formula ◽  
Natural Way

Abstract The Kerr-Schild form provides a natural way of realizing the classical double copy that relates exact solutions in general relativity to exact solutions in gauge theory. In this paper, we examine the asymptotic structure of Kerr-Schild form. In Newman-Unti gauge, we find a generic solution space satisfying the Kerr-Schild form in series expansion around null infinity. The news function in the solution space is chiral and can not lead to a mass loss formula. A class of asymptotically flat complex pp-wave solutions in closed form is obtained from the solution space.

scholarly journals The convolutional double copy: a case study with a point

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Andrés Luna ◽  
Silvia Nagy ◽  
Chris D. White
Keyword(s):  
Degrees Of Freedom ◽  
Point Of View ◽  
Classical Solutions ◽  
Recent Discussion ◽  
Schwarzschild Solution ◽  
Pure Gauge Theory ◽  
Gravity Theories ◽  
Double Copy ◽  
Two Parameter

AbstractThe double copy relates scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, and a number of approaches have been developed for doing so. One of these involves expressing fields in a variety of (super-)gravity theories in terms of convolutions of gauge fields, including also BRST ghost degrees of freedom that map neatly to their corresponding counterparts in gravity. In this paper, we spell out how to use the convolutional double copy to map gauge and gravity solutions in the manifest Lorenz and de Donder gauges respectively. We then apply this to a particular example, namely the point charge in pure gauge theory. As well as clarifying how to use the convolutional approach, our results provide an alternative point of view on a recent discussion concerning whether point charges map to the Schwarzschild solution, or the more general two-parameter JNW solution, which includes a dilaton field. We confirm the latter.

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