Chiral de Rham complex on special holonomy manifolds

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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48 pages

Scientific paper

Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We discuss classical and partial quantum results. As a concrete example, we construct two commuting copies of the Odake algebra (an extension of the N=2 superconformal algebra) on the space of global sections of CDR of a Calabi-Yau 3-fold. This is the first example of such a vertex subalgebra which is non-linearly generated by a finite number of superfields.

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