Cohomology of Lie Superalgebras: Forms, Integral Forms and Coset Superspaces
Abstract
We study ChevalleyEilenberg cohomology of physically relevant Lie superalgebras related to supersymmetric theories, providing explicit expressions for their cocycles in terms of their MaurerCartan forms. We then include integral forms in the picture by defining a notion of integral forms related to a Lie superalgebra. We develop a suitable generalization of ChevalleyEilenberg cohomology extended to integral forms and we prove that it is isomorphic to the ordinary ChevalleyEilenberg cohomology of the Lie superalgebra. Next we study equivariant ChevalleyEilenberg cohomology for coset superspaces, which plays a crucial role in supergravity and superstring models. Again, we treat explicitly several examples, providing cocycles' expressions and revealing a characteristic infinite dimensional cohomology.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 arXiv:
 arXiv:2012.05246
 Bibcode:
 2020arXiv201205246C
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 Added some references