Paper detail

Twists of superconformal algebras

We take first steps toward a theory of ``conformal twists'' for superconformal field theories in dimension 3 to 6, extending the well-known analysis of twists for supersymmetric theories. A conformal twist is a square-zero odd element in the superconformal Lie algebra, and we classify all twists and describe their orbits under the adjoint action of the superconformal group. 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 only discuss these subtleties in a few special cases. Conformal twists can give rise to interesting subalgebras and protected sectors of operators in a superconformal field theory, with the Donaldson--Witten topological field theory and the vertex operator algebras of 4-dimensional N=2 SCFTs being prominent examples. To obtain mathematical precision, we explain how to extract vertex algebras and E_n algebras from a twisted superconformal field theory using factorization algebras.