scholarly journals Symmetries of $$ \mathcal{N} $$ = (1, 0) supergravity backgrounds in six dimensions

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Sergei M. Kuzenko ◽  
Ulf Lindström ◽  
Emmanouil S. N. Raptakis ◽  
Gabriele Tartaglino-Mazzucchelli
Keyword(s):  
Killing Vector ◽  
Conformal Killing ◽  
Conformally Flat ◽  
Conformal Supergravity ◽  
Curved Space ◽  
Higher Symmetries ◽  
First Order ◽  
Supersymmetric Field Theories ◽  
Limited Class ◽  
Six Dimensions

Abstract General $$ \mathcal{N} $$ N = (1, 0) supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) SU(2) superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of supergravity backgrounds. In particular, we introduce the notion of a conformal Killing spinor superfield ϵα, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector ξa and tensor ζa(n) superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we introduce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal d’Alembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on a limited class of backgrounds, including all conformally flat ones.

Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves

2016 ◽  
Vol 13 (02) ◽  
pp. 1650015 ◽  
Author(s):  
Carlo Alberto Mantica ◽  
Young Jin Suh
Keyword(s):  
Symmetric Space ◽  
Weyl Tensor ◽  
Killing Vector ◽  
Complete Classification ◽  
Space Time ◽  
Conformal Killing ◽  
Conformally Flat ◽  
Conformal Curvature ◽  
Wave Space ◽  
Divergence Free

In this paper we present some new results about [Formula: see text]-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a covariantly constant we obtain a Brinkmann-wave. Anyway the metric results to be a subclass of the Kundt metric. Next we investigate pseudo-Z symmetric space-times with harmonic conformal curvature tensor: a complete classification of such spaces is obtained. They are necessarily quasi-Einstein and represent a perfect fluid space-time in the case of time-like associated covector; in the case of null associated covector they represent a pure radiation field. Further if the associated covector is locally a gradient we get a Brinkmann-wave space-time for [Formula: see text] and a pp-wave space-time in [Formula: see text]. In all cases an algebraic classification for the Weyl tensor is provided for [Formula: see text] and higher dimensions. Then conformally flat pseudo-Z symmetric space-times are investigated. In the case of null associated covector the space-time reduces to a plane wave and results to be generalized quasi-Einstein. In the case of time-like associated covector we show that under the condition of divergence-free Weyl tensor the space-time admits a proper concircular vector that can be rescaled to a time like vector of concurrent form and is a conformal Killing vector. A recent result then shows that the metric is necessarily a generalized Robertson–Walker space-time. In particular we show that a conformally flat [Formula: see text], [Formula: see text], space-time is conformal to the Robertson–Walker space-time.

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

CAUSAL BULK VISCOUS COSMOLOGIES IN CONFORMALLY FLAT SPACETIME

2000 ◽  
Vol 09 (04) ◽  
pp. 475-493 ◽  
Author(s):  
M. K. MAK ◽  
T. HARKO
Keyword(s):  
Large Time ◽  
Viscosity Coefficient ◽  
Approximate Solutions ◽  
Conformally Flat ◽  
First Order ◽  
Flat Spacetime ◽  
Bulk Viscous ◽  
Type Differential Equation ◽  
Bulk Viscosity Coefficient ◽  
Large Time Limit

The evolution of a causal bulk viscous cosmological fluid filled open conformally flat spacetime is considered. By means of appropriate transformations the equation describing the dynamics and evolution of the very early Universe can be reduced to a first order Abel type differential equation. In the case of a bulk viscosity coefficient proportional to the square root of the density, ξ~ρ1/2, an exact and two particular approximate solutions are obtained. The resulting cosmologies start from a singular state and generally have a noninflationary behavior, the deceleration parameter tending, in the large time limit, to zero. The thermodynamic consistency of the results is also checked.

Unitary vector fields are Fermi–Walker transported along Rytov–Legendre curves

2015 ◽  
Vol 12 (10) ◽  
pp. 1550111 ◽  
Author(s):  
Mircea Crasmareanu ◽  
Camelia Frigioiu
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Ricci Soliton ◽  
Conformal Killing ◽  
Space Forms ◽  
Potential Vector ◽  
Legendre Curves ◽  
Complex Space Forms

Fix ξ a unitary vector field on a Riemannian manifold M and γ a non-geodesic Frenet curve on M satisfying the Rytov law of polarization optics. We prove in these conditions that γ is a Legendre curve for ξ if and only if the γ-Fermi–Walker covariant derivative of ξ vanishes. The cases when γ is circle or helix as well as ξ is (conformal) Killing vector filed or potential vector field of a Ricci soliton are analyzed and an example involving a three-dimensional warped metric is provided. We discuss also K-(para)contact, particularly (para)Sasakian, manifolds and hypersurfaces in complex space forms.

Is the Massive Graviton a Viable Possibility?

2003 ◽  
Vol 18 (supp01) ◽  
pp. 329-339
Author(s):  
Antonios Papazoglou
Keyword(s):  
Cosmological Constant ◽  
Brane World ◽  
Massive Graviton ◽  
Curved Space ◽  
Negative Cosmological Constant ◽  
World Theory ◽  
Six Dimensions

In this talk we discuss the scenario of multigravity according to which the gravity we observe in intermediate scales (1 mm < r < 1026 cm ) is mediated by both a massless graviton and one or more of ultralight spin-2 state. We present how this can be realized in a five dimensional brane-world theory with flat branes and the complications associated with the extra polarizations of the massive gravitons (van Dam-Veltman-Zakharov discontinuity) and the ghost radions corresponding to the fluctuations of the negative tension branes present in these models. We then show how we can construct models of AdS4 branes instead with exclusively positive tension and demonstrate how the van Dam-Veltman-Zakharov no-go theorem can be circumvented in curved space. These models, although they are consistent, face phenomenological problems related to the presence of a remnant negative cosmological constant on the branes. We finally present how we can obtain the same constructions in six dimensions with flat positive tensions branes only, in a manner that they are both theoretically consistent and phenomenologically acceptable. The latter come in two copies each and offer the first problem-free realization of the multigravity scenario.

scholarly journals NAMBU-JONA-LASINIO MODEL IN CURVED SPACE-TIME

1993 ◽  
Vol 08 (22) ◽  
pp. 2117-2123 ◽  
Author(s):  
T. INAGAKI ◽  
T. MUTA ◽  
S.D. ODINTSOV
Keyword(s):  
Proper Time ◽  
Space Time ◽  
Leading Order ◽  
Coupling Constant ◽  
Normal Coordinate ◽  
Dynamical Mass ◽  
Curved Space ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase

The phase structure of Nambu-Jona-Lasinio model with N-component fermions in curved space-time is studied in the leading order of the 1/N expansion. The effective potential for composite operator [Formula: see text] is calculated by using the normal coordinate expansion in the Schwinger proper-time method. The existence of the first order phase transition caused by the change of the space-time curvature is confirmed and the dynamical mass of the fermion is calculated as a simultaneous function of the curvature and the four-fermion coupling constant. The phase diagram in the curvature and the coupling constant is obtained.

Symmetry operators for Maxwell’s equations on curved space-time

1992 ◽  
Vol 439 (1905) ◽  
pp. 103-113 ◽  
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Separation Of Variables ◽  
Sufficient Conditions ◽  
Symmetry Operator ◽  
Space Time ◽  
Conformal Killing ◽  
Curved Space ◽  
Background Space ◽  
Necessary And Sufficient

We derive necessary and sufficient conditions that a second-order co-variant differential operator be a symmetry operator of Maxwell’s equations in a general curved space-time background. It is found that such operators are naturally formulated in terms of conformal Killing vectors, tensors and spinors. Operators of this type play a role in the solution of Maxwell’s equations via separation of variables in the Kerr background space-time.

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