A vertex algebra attached to the flag manifold and Lie algebra cohomology

T. Arakawa; F. Malikov

doi:10.1063/1.3460161

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arXiv · 0911.0922

A vertex algebra attached to the flag manifold and Lie algebra cohomology

T. Arakawa·F. Malikov

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Abstract

Each flag manifold carries a unique algebra of chiral differential operators. Continuing along the lines of arXiv:0903.1281 we compute the vertex algebra structure on the cohomology of this algebra. The answer is: the tensor product of the center and a subalgebra; the center is isomorphic, as a commutative associative algebra, to the cohomology of the corresponding maximal nilpotent Lie algebra; the subalgebra is the vacuum module over the corresponding affine Lie algebra of critical level and 0 central character. We next find the Friedan-Martinec-Shenker-Borisov bosonization of the cohomology algebra in case of the projective line and show that this algebra vanishes nonperturbatively, thus verifying a suggestion by Witten.

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BibTeX RIS

T. Arakawa, F. Malikov. 2009-11-16. A vertex algebra attached to the flag manifold and Lie algebra cohomology. https://doi.org/10.1063/1.3460161

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