We propose a physical interpretation of the chiral de Rham complex
as a formal Hamiltonian quantization of the supersymmetric non-linear
sigma model. We show that the chiral de Rham complex on a Calabi–Yau
manifold carries all information about the classical dynamics of the sigma
model. Physically, this provides an operator realization of the non-linear
sigma model. Mathematically, the idea suggests the use of Hamiltonian
flow equations within the vertex algebra formalism with the possibility to
incorporate both left and right moving sectors within one mathematical
framework.