Solving the 3D Ising Model with the Conformal Bootstrap

In recent years the conformal bootstrap has emerged as a surprisingly powerful tool to study CFTs in dimensions greater than two.  In this talk I will explain how crossing symmetry of the four-point function of scalar operators can be used to extract very non-trivial constraints on the spectrum of a putative CFT in arbitrary spacetime dimension.  Applying these techniques in D=3 we will find that the 3D Ising model lies at a special point in the space of CFTs.  Moreover, we will show that constraints from conformal invariance can be used to significantly reduce the error in the known estimates for the dimensions of operators and suggest a method to generalize this to a compute the dimensions and OPE coefficients of far more operators in the theory.  Time permitting I will mention some more general applications of this technology, including holography.