Applications of the bootstrap to superconformal field theories require the construction of superconformal blocks for four-point functions of arbitrary supermultiplets. Up until recently, only sporadic results had been obtained. In my talk I explain the key ingredients of a new systematic construction that apply to a large class of superconformal field theories, including 4-dimensional models with any number N of supersymmetries. It hinges on a universal construction of the relevant Casimir differential equations. In order to find these equations, we model superconformal blocks as functions on the supergroup and pick a distinguished set of coordinates. The latter are chosen so that the superconformal Casimir operator can be written as a perturbation of the Casimir operator for spinning bosonic blocks by a fermionic (nilpotent) term. Solutions to the associated eigenvalue problem can be obtained through a quantum mechanical perturbation theory that truncates at some finite order so that all results are exact.
Slava Rychkov
