Killing spinor
Type of Dirac operator eigenspinor From Wikipedia, the free encyclopedia
Type of Dirac operator eigenspinor From Wikipedia, the free encyclopedia
Killing spinor is a term used in mathematics and physics.
By the more narrow definition, commonly used in mathematics, the term Killing spinor indicates those twistor spinors which are also eigenspinors of the Dirac operator.[1][2][3] The term is named after Wilhelm Killing.
Another equivalent definition is that Killing spinors are the solutions to the Killing equation for a so-called Killing number.
More formally:[4]
In physics, Killing spinors are used in supergravity and superstring theory, in particular for finding solutions which preserve some supersymmetry. They are a special kind of spinor field related to Killing vector fields and Killing tensors.
If is a manifold with a Killing spinor, then is an Einstein manifold with Ricci curvature , where is the Killing constant.[5]
If is purely imaginary, then is a noncompact manifold; if is 0, then the spinor field is parallel; finally, if is real, then is compact, and the spinor field is called a ``real spinor field."
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