scholarly journals The classical double copy for half-maximal supergravities and T-duality

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Stephen Angus ◽  
Kyoungho Cho ◽  
Kanghoon Lee
Keyword(s):  
Equations Of Motion ◽  
Null Model ◽  
Linear Structure ◽  
Single Copy ◽  
Duality Transformations ◽  
Double Field Theory ◽  
Highly Nonlinear ◽  
Scalar Theories ◽  
Double Copy ◽  
Kaluza Klein

Abstract We study the classical double copy for ungauged half-maximal supergravities using the Kaluza-Klein reduction of double field theory (DFT). We construct a general formula for the Kaluza-Klein (KK) reduction of the DFT Kerr-Schild ansatz. The KK reduction of the ansatz is highly nonlinear, but the associated equations of motion are linear. This linear structure implies that half-maximal supergravities admit a classical double copy. We show that their single copy is given by a pair of Maxwell-scalar theories, which are the KK reduction of a higher-dimensional single copy of DFT. We also investigate their T-duality transformations — both the Buscher rule and continuous O(D, D) rotations. Applying the Buscher rule to the Kerr BH, we obtain a solution with a nontrivial Kalb-Ramond field and dilaton. We also identify the single copy of Sen’s heterotic BH and the chiral null model and show that the chiral null model is self-dual under T-duality rotations.

scholarly journals Supergravity solution-generating techniques and canonical transformations of σ-models from O(D, D)

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Riccardo Borsato ◽  
Sibylle Driezen
Keyword(s):  
Field Theory ◽  
Equations Of Motion ◽  
Canonical Transformations ◽  
Strong Constraint ◽  
Duality Transformations ◽  
Double Field Theory ◽  
Supergravity Solution

Abstract Within the framework of the flux formulation of Double Field Theory (DFT) we employ a generalised Scherk-Schwarz ansatz and discuss the classification of the twists that in the presence of the strong constraint give rise to constant generalised fluxes interpreted as gaugings. We analyse the various possibilities of turning on the fluxes Hijk, Fijk, Qijk and Rijk, and the solutions for the twists allowed in each case. While we do not impose the DFT (or equivalently supergravity) equations of motion, our results provide solution-generating techniques in supergravity when applied to a background that does solve the DFT equations. At the same time, our results give rise also to canonical transformations of 2-dimensional σ-models, a fact which is interesting especially because these are integrability-preserving transformations on the worldsheet. Both the solution-generating techniques of supergravity and the canonical transformations of 2-dimensional σ-models arise as maps that leave the generalised fluxes of DFT and their flat derivatives invariant. These maps include the known abelian/non-abelian/Poisson-Lie T-duality transformations, Yang-Baxter deformations, as well as novel generalisations of them.

scholarly journals Non-Riemannian gravity actions from double field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
A. D. Gallegos ◽  
U. Gürsoy ◽  
S. Verma ◽  
N. Zinnato
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Technical Note ◽  
Action Principle ◽  
Relativistic Symmetry ◽  
Gravitational Theories ◽  
Double Field Theory

Abstract Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with non-relativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.

scholarly journals On polytopes and generalizations of the KLT relations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nikhil Kalyanapuram
Keyword(s):  
Scattering Amplitudes ◽  
Large Class ◽  
Moduli Space ◽  
Differential Forms ◽  
Natural Generalization ◽  
Intersection Theory ◽  
Hyperplane Arrangements ◽  
Number Of Solutions ◽  
Scalar Theories ◽  
Double Copy

Abstract We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT). To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on ℳ0, n — the moduli space of marked Riemann spheres — the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

scholarly journals The classical double copy for M-theory from a Kerr-Schild ansatz for exceptional field theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
David S. Berman ◽  
Kwangeon Kim ◽  
Kanghoon Lee
Keyword(s):  
Field Theory ◽  
State Of The Art ◽  
Single Copy ◽  
Current State ◽  
M Theory ◽  
Double Copy

Abstract We construct the classical double copy formalism for M-theory. This extends the current state of the art by including the three form potential of eleven dimensional supergravity along with the metric. The key for this extension is to construct a Kerr-Schild type Ansatz for exceptional field theory. This Kerr-Schild Ansatz then allows us to find the solutions of charged objects such as the membrane from a set of single copy fields. The exceptional field theory formalism then automatically produces the IIB Kerr-Schild ansatz allowing the construction of the single copy for the fields of IIB supergravity (with manifest SL(2) symmetry).

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.

Tilt-Wing Rotorcraft Dynamic Analysis Using Multibody Formulation

1992 ◽  
Author(s):  
Patrick J. O’Heron ◽  
Parviz E. Nikravesh ◽  
Ara Arabyan ◽  
Donald L. Kunz
Keyword(s):  
Flight Control ◽  
High Speed ◽  
Equations Of Motion ◽  
Flight Path ◽  
Minimal Set ◽  
Near Wake ◽  
Highly Nonlinear ◽  
Nonlinear Transient ◽  
Nonlinear Transient Dynamics ◽  
Rotor Assembly

Abstract A model is presented that can be used to simulate the highly nonlinear transient dynamics associated with advanced rotorcraft conversion processes. Multibody equations of motion of the fuselage, the tilting wing, and the rotor assembly are derived using a minimal set of coordinates. An enhanced aerodynamics model is employed to account for unsteadiness and nonlinearity in the near-wake aerodynamics, with a dynamic uniform inflow to compute the far-wake aerodynamics, and a flight control system is employed to compute the blade pitch settings that are necessary to achieve a desired flight path. The model is subjected to a demanding flight path simulation to illustrate that it can perform vertical take-off, hover, tilt-wing conversion, and high-speed forward flight maneuvers effectively.

Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Alexander Olshevskiy ◽  
Oleg Dmitrochenko ◽  
Chang-Wan Kim
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Test Problems ◽  
Absolute Nodal Coordinate ◽  
Highly Nonlinear ◽  
Brick Element ◽  
The Absolute

The present paper contributes to the field of flexible multibody systems dynamics. Two new solid finite elements employing the absolute nodal coordinate formulation are presented. In this formulation, the equations of motion contain a constant mass matrix and a vector of generalized gravity forces, but the vector of elastic forces is highly nonlinear. The proposed solid eight node brick element with 96 degrees of freedom uses translations of nodes and finite slopes as sets of nodal coordinates. The displacement field is interpolated using incomplete cubic polynomials providing the absence of shear locking effect. The use of finite slopes describes the deformed shape of the finite element more exactly and, therefore, minimizes the number of finite elements required for accurate simulations. Accuracy and convergence of the finite element is demonstrated in nonlinear test problems of statics and dynamics.

Melnikov-based analysis for chaotic dynamics of spin-orbit motion of a gyrostat satellite

2019 ◽  
Vol 233 (4) ◽  
pp. 931-941
Author(s):  
Seyed Mahdi Abtahi
Keyword(s):  
Equations Of Motion ◽  
Time History ◽  
Melnikov Method ◽  
Spin Orbit ◽  
Attitude Dynamics ◽  
Inertia Moment ◽  
Coupled Equations ◽  
Highly Nonlinear ◽  
Complex Spin ◽  
The Mathematical Model

Interactions of the orbital motion on attitude dynamics of the gyrostat satellite are considered in this paper. The mathematical model is derived using the Hamiltonian method for the spin-orbit motion of the spacecraft followed by the reduction of the coupled equations of motion using the extended Deprit canonical transformation. The analytical Melnikov method is used innovatively to study chaos on the complex Spin-Orbit dynamics of the gyrostat satellite. Also, the numerical methods such as Lyapunov exponent criterion, Poincaré section, trajectories of phase portrait, and the time–history responses can be proved the heteroclinic bifurcation and chaotic vibrations in the highly nonlinear system. Using the results based on the Melnikov integral, the parameters of the spacecraft including the mass and inertia moment of satellite with respect to the altitude of orbit can be designed in order to control the bifurcation with a view to prevention of chaos in the system in the absence of an active control system.

Sign in / Sign up

Export Citation Format

Share Document