Advances in Theoretical and Mathematical Physics

Volume 13 (2009)

Number 4

Non-linear sigma models via the chiral de Rham complex

Pages: 1221 – 1254



Joel Ekstrand

Reimundo Heluani

Johan Källén

Maxim Zabzine


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.

Published 1 January 2009