Operators on pure spinor spaces

Paper in proceeding, 2009

Pure spinors are relevant to the formulation of supersymmetric theories, and provide the only known way to maintain manifest maximal supersymmetry. The (non-linear) pure spinor constraint makes it nontrivial to find well defined operators on pure spinor wave functions. We discuss how such operators are defined. One application concerns covariant gauge fixing in maximally supersymmetric Yang-Mills (and string theory). Another issue is the construction of a manifestly supersymmetric action for 11-dimensional supergravity in terms of a scalar superfield. We describe some work in progress. This is the written version of a talk given at the 4th International Sakharov Conference in Physic, Moscow, May 2009 and at the 8th International Workshop “Lie Theory and its Applications in Physics”, Varna, June 2009.