Perturbation theory
The above string action has a conformal invariance. This is a property of a two dimensional Riemannian manifold. At the quantum level, this property is lost due to anomalies and the theory itself is not consistent, having no unitarity. So it is necessary to require that conformal invariance is kept at any order of perturbation theory. Perturbation theory is the only known approach to manage the quantum field theory. Indeed, the beta functions at two loops are