Twists of superconformal algebras

We develop the theory of ``conformal twists'' of superconformal field theories in dimensions 3 to 6, extending the well-known analysis of twists for supersymmetric theories. The conformal twists describe all possible inequivalent choices of a nilpotent element in the superconformal algebra. Such twists can give rise to interesting subalgebras and protected sectors of operators, with the Donaldson--Witten topological field theory and the vertex operator algebras of 4-dimensional N=2 SCFTs being prominent examples. We work mostly with the complexified superconformal algebras, unless explicitly stated otherwise; real forms of the superconformal algebra may have important physical implications, but we leave these subtleties to future work. To obtain mathematical precision, we explain how to extract vertex algebras and Eₙ algebras from a twisted superconformal field theory using factorization algebras.