scholarly journals Weyl doubling

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rashid Alawadhi ◽  
David S. Berman ◽  
Bill Spence
Keyword(s):  
Field Strength ◽  
Flat Space ◽  
Brane World ◽  
Gauge Fields ◽  
Weyl Spinor ◽  
Type D ◽  
Spacetime Curvature ◽  
World Volume ◽  
Abelian Field ◽  
Double Copy

Abstract We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the field strength and the Weyl tensor, following the Weyl spinor double copy relation. However, we diverge from the usual double copy paradigm by taking the gauge fields to be in the curved spacetime as opposed to an auxiliary flat space.We show how for Gibbons-Hawking spacetimes with more than two centres a generalisation of the Weyl doubling formula is needed by including a derivative-dependent expression which is linear in the Abelian field strength. We also find a type of twisted doubling formula in a case of a manifold with Spin(7) holonomy in eight dimensions.For Einstein Maxwell theories where there is an independent gauge field defined on spacetime, we investigate how the gauge fields determine the Weyl spacetime curvature via a doubling formula. We first show that this occurs for the Reissner-Nordström metric in any dimension, and that this generalises to the electrically-charged Born-Infeld solutions. Finally, we consider brane systems in supergravity, showing that a similar doubling formula applies. This Weyl formula is based on the field strength of the p-form potential that minimally couples to the brane and the brane world volume Killing vectors.

scholarly journals From Navier-Stokes to Maxwell via Einstein

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Cynthia Keeler ◽  
Tucker Manton ◽  
Nikhil Monga
Keyword(s):  
Potential Flow ◽  
Single Copy ◽  
Navier Stokes ◽  
Gauge Fields ◽  
Type Ii ◽  
Type D ◽  
Potential Flows ◽  
Constant Vorticity ◽  
Gravity Duality ◽  
Double Copy

Abstract We revisit the cutoff surface formulation of fluid-gravity duality in the context of the classical double copy. The spacetimes in this fluid-gravity duality are algebraically special, with Petrov type II when the spacetime is four dimensional. We find two special classes of fluids whose dual spacetimes exhibit higher algebraic speciality: constant vorticity flows have type D gravity duals, while potential flows map to type N spacetimes. Using the Weyl version of the classical double copy, we construct associated single-copy gauge fields for both cases, finding that constant vorticity fluids map to a solenoid gauge field. Additionally we find the scalar in a potential flow fluid maps to the zeroth copy scalar.

scholarly journals WORLD VOLUME SOLITONS OF THE D3-BRANE IN THE BACKGROUND OF (p, q) FIVE-BRANES

2000 ◽  
Vol 15 (28) ◽  
pp. 4477-4498 ◽  
Author(s):  
P. M. LLATAS ◽  
A. V. RAMALLO ◽  
J. M. SÁNCHEZ DE SANTOS
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Brane World ◽  
Invariant Solutions ◽  
First Order ◽  
World Volume ◽  
The World ◽  
Energy Bound

We analyze the world volume solitons of a D3-brane probe in the background of parallel (p, q) five-branes. The D3-brane is embedded along the directions transverse to the five-branes of the background. By using the S duality invariance of the D3-brane, we find a first-order differential equation whose solutions saturate an energy bound. The SO(3) invariant solutions of this equation are found analytically. They represent world volume solitons which can be interpreted as formed by parallel (-q, p) strings emanating from the D3-brane world volume. It is shown that these configurations are 1/4 supersymmetric and provide a world volume realization of the Hanany–Witten effect.

scholarly journals GAUSS DECOMPOSITION, WAKIMOTO REALIZATION AND GAUGED WZNW MODELS

1994 ◽  
Vol 09 (11) ◽  
pp. 1009-1023
Author(s):  
H. ARFAEI ◽  
N. MOHAMMEDI
Keyword(s):  
Field Strength ◽  
Sigma Model ◽  
Target Space ◽  
Gauge Fields ◽  
Nonlinear Sigma Model ◽  
Model Interpretation ◽  
Gauss Decomposition ◽  
Wznw Model ◽  
Wakimoto Realization

The implications of gauging the Wess-Zumino-Novikov-Witten (WZNW) model using the Gauss decomposition of the group elements are explored. We show that, contrary to the standard gauging of WZNW models, this gauging is carried out by minimally coupling the gauge fields. We find that this gauging, in the case of gauging and Abelian vector subgroup, differs from the standard one by terms proportional to the field strength of the gauge fields. We prove that gauging an Abelian vector subgroup does not have a nonlinear sigma model interpretation. This is because the target-space metric resulting from the integration over the gauge fields is degenerate. We demonstrate, however, that this kind of gauging has a natural interpretation in terms of Wakimoto variables.

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 "Gravitationally Lensed Gravitation" (GLG)

2021 ◽  
Author(s):  
Andreas Boenke
Keyword(s):  
General Relativity ◽  
Field Strength ◽  
Free Fall ◽  
Gravitational Effect ◽  
Gravitational Lens ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Optical Illusions ◽  
Spacetime Curvature ◽  
Background Object

The intention of this paper is to point out a remarkable hitherto unknown effect of General Relativity. Starting from fundamental physical principles and phenomena arising from General Relativity, it is demonstrated by a simple Gedankenexperiment that a gravitational lens enhances not only the light intensity of a background object but also its gravitational field strength by the same factor. Thus, multiple images generated by a gravitational lens are not just optical illusions, they also have a gravitational effect at the location of the observer! The "Gravitationally Lensed Gravitation" (GLG) may help to better understand the rotation curves of galaxies since it leads to an enhancement of the gravitational interactions of the stars. Furthermore, it is revealed that besides a redshift of the light of far distant objects, the cosmic expansion also causes a corresponding weakening of their gravitational effects. The explanations are presented entirely without metric representation and tensor formalism. Instead, the behavior of light is used to indicate the effect of spacetime curvature. The gravitation is described by the field strength which is identical to the free fall acceleration. The new results thus obtained provide a reference for future numerical calculations based on the Einstein field equations.

scholarly journals ON GAUGE DYNAMICS AND SUSY BREAKING IN ORIENTIWORLD

2002 ◽  
Vol 17 (27) ◽  
pp. 3875-3895
Author(s):  
ZURAB KAKUSHADZE
Keyword(s):  
Crucial Role ◽  
Dimensional Space ◽  
Susy Breaking ◽  
Brane World ◽  
The Other ◽  
Quantum Level ◽  
Rich Variety ◽  
World Volume ◽  
The Standard Model ◽  
Dimensional Gravity

In the orientiworld framework the Standard Model fields are localized on D3-branes sitting on top of an orientifold three-plane. The transverse six-dimensional space is a noncompact orbifold (or a more general conifold). The four-dimensional gravity on D3-branes is reproduced due to the four-dimensional Einstein–Hilbert term induced at the quantum level. The orientifold three-plane plays a crucial role, in particular, without it the D3-brane world-volume theories would be conformal due to the tadpole cancellation. We study nonperturbative gauge dynamics in various [Formula: see text] supersymmetric orientiworld models based on the Z3 as well as Z5 and Z7 orbifold groups. Our discussions illustrate that there is a rich variety of supersymmetry preserving dynamics in some of these models. On the other hand, we also find some models with dynamical supersymmetry breaking.

scholarly journals TOPOLOGICALLY MASSIVE GAUGE THEORY: A LORENTZIAN SOLUTION

2007 ◽  
Vol 22 (16n17) ◽  
pp. 2961-2976 ◽  
Author(s):  
K. SAYGILI
Keyword(s):  
Field Equation ◽  
Gauge Theory ◽  
Field Strength ◽  
Gauge Transformation ◽  
Global Section ◽  
Gauge Potential ◽  
Abelian Gauge ◽  
Abelian Field ◽  
Hopf Map ◽  
Topological Mass

We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space [Formula: see text] by means of an SU (1, 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass ν ~ ng2. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge transformation. Then we present map [Formula: see text] including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of [Formula: see text] as a trivial [Formula: see text] bundle over the upper portion of the pseudosphere [Formula: see text] which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto [Formula: see text] using a global section of the solution on [Formula: see text]. Then we discuss the integration of the field equation using the Archimedes map [Formula: see text]. We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on [Formula: see text].

scholarly journals Antisymmetric tensor gauge fields on S4

2004 ◽  
Vol 82 (7) ◽  
pp. 541-548
Author(s):  
D.G.C. McKeon
Keyword(s):  
Field Model ◽  
Free Field ◽  
Flat Space ◽  
Antisymmetric Tensor ◽  
Gauge Fields ◽  
Scalar Model ◽  
Abelian Gauge ◽  
Five Dimensions ◽  
Higher Dimensional

Antisymmetric tensor gauge fields ϕab(η) are formulated on the surface of a sphere S4(η2 = a2) embedded in five dimensions. Such compact manifolds occur in the dimensional reduction of higher dimensional spaces that naturally occur in string theories. The free field model is equivalent to a scalar model on this sphere. Interactions with gauge fields are discussed. It is feasable to formulate models for interactions with U(1) gauge fields Aa(η) that are akin to those of Freedman and Townsend in flat space. In addition, it proves possible to have a novel interaction of ϕab with Aa and a spinor field Ψ(η) on S4 with both Abelian and non-Abelian gauge invariance. In these models, Aa plays the role of a Stueckelberg field.PACS No.: 11.30.Ly

scholarly journals "SELF-TUNING" AND CONFORMALITY

2000 ◽  
Vol 15 (30) ◽  
pp. 1879-1890 ◽  
Author(s):  
ZURAB KAKUSHADZE
Keyword(s):  
Brane World ◽  
Infinite Volume ◽  
Brane Tension ◽  
Codimension One ◽  
World Volume ◽  
Self Tuning ◽  
Flat Solution ◽  
Range Of Values ◽  
Continuous Range ◽  
Tuning Property

We consider an infinite-volume brane world setup where a codimension one-brane is coupled to bulk gravity plus a scalar field with vanishing potential. The latter is protected by bulk supersymmetry, which is intact even if brane supersymmetry is completely broken as the volume of the extra dimension is infinite. Within this setup we discuss a flat solution with a "self-tuning" property, i.e. such a solution exists for a continuous range of values for the brane tension. This infinite-volume solution is free of any singularities, and has the property that the brane cosmological constant is protected by bulk supersymmetry. We, however, also point out that consistency of the coupling between bulk gravity and brane matter generically appears to require that the brane world-volume theory be conformal.

A BRST APPROACH TO MASSLESS GAUGE FIELDS OF INTEGER SPIN

1990 ◽  
Vol 05 (16) ◽  
pp. 3247-3264
Author(s):  
THOMAS DOMEIJ
Keyword(s):  
Wave Function ◽  
Symmetric Tensor ◽  
Flat Space ◽  
Gauge Fields ◽  
Arbitrary Integer ◽  
Massless Particles ◽  
Gauge Invariant ◽  
Function Representation ◽  
Integer Spin ◽  
Do So

We present a method based on BRST techniques for how to obtain the conventional equations for symmetric tensor gauge fields which describe free massless particles of arbitrary integer spin. We do so in a wave function representation in a flat space-time background of any dimension. A fairly straightforward way is also presented for how to obtain the equations from a gauge invariant Lagrangian of the form [Formula: see text].

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