Pure spinor

<p>In the domain of <a href="/facts/Mathematics/pxTouaz4">mathematics</a> known as <a href="/facts/Representation_theory/3ydLtaGH">representation theory</a>, pure spinors (or simple spinors) are <a href="/facts/Spinor/sKFNnEwP">spinors</a> that are annihilated, under the <a href="/facts/Clifford_algebra/qnqSCz5h">Clifford algebra representation</a>, by a <a href="/facts/Quadric_(algebraic_geometry)/eCG83ks3">maximal isotropic subspace</a> of a vector space 
  
    
      
        V
      
    
    {\displaystyle V}
  
 with respect to a scalar product 
  
    
      
        Q
      
    
    {\displaystyle Q}
  
.  
They were introduced by <a href="/facts/%25C3%2589lie_Cartan/Uvhkp66S">Élie Cartan</a> in the 1930s and further developed by <a href="/facts/Claude_Chevalley/MJvMYE34">Claude Chevalley</a>. 
</p><p>They are a key ingredient in the study of <a href="/facts/Spin_structure/BF78kFz8">spin structures</a> and higher dimensional generalizations of <a href="/facts/Twistor_theory/DrtqvKCs">twistor theory</a>, introduced by <a href="/facts/Roger_Penrose/r4mlrFUH">Roger Penrose</a> in the 1960s. 
They have been applied to the study of <a href="/facts/N_%253D_4_supersymmetric_Yang%25E2%2580%2593Mills_theory/RuCTjozP">supersymmetric Yang-Mills theory</a> in 10D,  <a href="/facts/Superstring_theory/1gY26F0D">superstrings</a>,  <a href="/facts/Generalized_complex_structures/6YbgacPA">generalized complex structures</a>
  and  parametrizing solutions of <a href="/facts/Integrable_system/Crgzjw6G">integrable hierarchies</a>.
</p>

Pure spinor open-in-new

Pure spinor