Large-parameter limits of conformal blocks

Abstract

Conformally invariant quantum field theories can be “bootstrapped” because they can be defined without reference to a Lagrangian or a Hamiltonian. When they are instead defined in terms of spins and scaling dimensions of local operators, much of the parameter space can be ruled out as unphysical. We review recent results about conformal blocks — special functions important in these numerical studies. Our new result is that they approach monomials as the dimension difference between two operators becomes large. We also discuss the case of large space–time dimension and the question of which limits are useful for the bootstrap.