killing spinor

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. 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:

A Killing spinor on a manifold M is a spinor field

\phi

which satisfies

\nabla_X\phi=\lambda X\cdot\phi

for all tangent vectors X, where

\nabla

is the spinor covariant derivative,

\cdot

is Clifford multiplication and

\lambda

is a constant, called the Killing number. If

\lambda=0

then the spinor is called a parallel spinor.

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.

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