Supergravity backgrounds and symmetry superalgebras

Ertem, Ümit

doi:10.3906/fiz-1510-8

Cited by 3 publications

(4 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…then it is easy to find the differential equations satisfied by the bilinears of the Killing spinor in the presence of torsion which is discussed in appendix C [18,19]. For even values of p these are given by…”

Section: The Investigation Of Membrane Motions In a Specific Non-riem...mentioning

confidence: 99%

Motion of membranes in space-times with torsion

Açık¹,

Çatalkaya²,

Ertem³

et al. 2019

Class. Quantum Grav.

View full text Add to dashboard Cite

The motion of membranes interacting with external fields in space-times with curvature and torsion is considered. The intrinsic and extrinsic properties of the immersion are fused together to form a stress tensor for the corresponding material hypersurface. This geometro-elastic stress tensor is part of the total stress tensor by which it looses the symmetry and divergenceless properties because of the existence of torsion. The equation of motion of the membrane is given by equating the total stress tensor to a non-zero value determined by the curvature and torsion of the ambient space-time. Dirac andÖnder-Tucker bubbles are considered as special cases. An example of the membrane motion on a manifold admitting a generalized Killing spinor is given.

show abstract

Section: The Investigation Of Membrane Motions In a Specific Non-riem...mentioning

confidence: 99%

Motion of membranes in space-times with torsion

Açık¹,

Çatalkaya²,

Ertem³

et al. 2019

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…Moreover, a subset of CKY forms that are called normal CKY forms also satisfy a Lie superalgebra structure in Einstein manifolds. The normal CKY forms satisfy the following integrability condition besides the CKY equation defined in (20)…”

Section: Cky Superalgebrasmentioning

confidence: 99%

“…For the case of conformal Killing vector fields and twistor spinors, one can also construct Lie superalgebras which are called conformal superalgebras by adding some extra R-symmetry generators [19]. The structure of Killing and conformal superalgebras can be extended to include KY forms and CKY forms respectively by using the graded Lie algebra structure of hidden symmetries and the symmetry operators of Killing and twistor spinors [8,12,20]. Although they constitute a superalgebra structure, they do not correspond to Lie superalgebras.…”

Section: Introductionmentioning

confidence: 99%

Rigidity of Killing-Yano and conformal Killing-Yano superalgebras

Ertem¹

2017

Preprint

Self Cite

View full text Add to dashboard Cite

Symmetry algebras of Killing vector fields and conformal Killing vectors fields can be extended to Killing-Yano and conformal Killing-Yano superalgebras in constant curvature manifolds. By defining Z-gradations and filtrations of these superalgebras, we show that the second cohomology groups of them are trivial and they cannot be deformed to other Lie superalgebras. This shows the rigidity of Killing-Yano and conformal Killing-Yano superalgebras and reveals the fact that they correspond to geometric invariants of constant curvature manifolds. We discuss the structures and dimensions of these superalgebras on AdS spacetimes as examples.

show abstract

“…Relations between harmonic spinors and twistor spinors are used to obtain the solutions of the Seiberg-Witten equations by generalizing these relations to the gauged case [32,33]. Supergravity Killing spinors which arise as the supersymmetry generators of supergravity theories are connected to the parallel and Killing spinors for different flux choices in the relevant theory and the solutions of the massless field equations for different spin particles are connected to each other via spin raising and lowering methods by using twistor spinors [34,35,36]. Moreover, the derivation of the periodic table of topological insulators and superconductors via Clifford algebra chessboard and the index of Dirac operators is also discussed [25].…”

Section: Introductionmentioning

confidence: 99%

Spin Geometry and Some Applications

Ertem¹

2018

Preprint

Self Cite

View full text Add to dashboard Cite

In this review, basic definitions of spin geometry are given and some of its applications to supersymmetry, supergravity and condensed matter physics are summarized. Clifford algebras and spinors are defined and the first-order differential operators on spinors which lead to the definitions of twistor and Killing spinors are discussed. Holonomy classification for manifolds admitting parallel and Killing spinors are given. Killing-Yano and conformal Killing-Yano forms resulting from the spinor bilinears of Killing and twistor spinors are introduced and the symmetry operators of special spinor equations are constructed in terms of them. Spinor bilinears and symmetry operators are used for constructing the extended superalgebras from twistor and Killing spinors. A method to obtain harmonic spinors from twistor spinors and potential forms is given and its implications on finding solutions of the Seiberg-Witten equations are discussed. Supergravity Killing spinors defined in bosonic supergravity theories are considered and possible Lie algebra structures satisfied by their spinor bilinears are examined. Spin raising and lowering operators for massless field equations with different spins are constructed and the case for Rarita-Schwinger fields is investigated. The derivation of the periodic table of topological insulators and superconductors in terms of Clifford chessboard and index of Dirac operators is summarized.

show abstract

Supergravity backgrounds and symmetry superalgebras

Cited by 3 publications

References 45 publications

Motion of membranes in space-times with torsion

Motion of membranes in space-times with torsion

Rigidity of Killing-Yano and conformal Killing-Yano superalgebras

Spin Geometry and Some Applications

Contact Info

Product

Resources

About