The chiral de Rham complex and quantum non-linear sigma models

Abstract

In [J. Ekstrand, R. Heluani, J. Kallen, M. Zabzine, Adv. Theor. Math. Phys. 13 (2009) 1221-1254; J. Ekstrand, R. Heluani, J. Kallen, M. Zabzine, arXiv:1003.4388 [hep-th] ], the interpretation of the chiral de Rham complex as a formal quantization of 2d non-linear sigma models in the Hamiltonian framework was suggested and used to compute symmetry algebras for quantum models with non-flat target spaces. Here we review the construction.