Mathematics – Algebraic Geometry
Scientific paper
2009-11-04
Mathematics
Algebraic Geometry
a reference added
Scientific paper
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.
Arakawa Tomoyuki
Malikov Fyodor
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