Non-linear sigma models via the chiral de Rham complex

TL;DR

This paper interprets the chiral de Rham complex as a quantization of the supersymmetric non-linear sigma model, linking physical dynamics with a mathematical vertex algebra framework on Calabi-Yau manifolds.

Contribution

It introduces a novel physical interpretation of the chiral de Rham complex as a Hamiltonian quantization of the sigma model, unifying left and right sectors mathematically.

Findings

Chiral de Rham complex encodes classical sigma model dynamics.

Provides an operator realization of the non-linear sigma model.

Suggests Hamiltonian flow equations in vertex algebra formalism.

Abstract

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.