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We propose a physical interpretation of the chiral de Rham complex as aformal Hamiltonian quantization of the supersymmetric non-linear sigma model.We show that the chiral de Rham complex on a Calabi-Yau manifold carries allinformation about the classical dynamics of the sigma model. Physically, thisprovides an operator realization of the non-linear sigma model. Mathematically,the idea suggests the use of Hamiltonian flow equations within the vertexalgebra formalism with the possibility to incorporate both left and rightmoving sectors within one mathematical framework.

Non-linear sigma models via the chiral de Rham complex