Each flag manifold carries a unique algebra of chiral differential operators. Continuing along th... more 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.
... Here Lie(V ) denotes the Lie algebra of Fourier components of the fields of V . ... CHIRAL PO... more ... Here Lie(V ) denotes the Lie algebra of Fourier components of the fields of V . ... CHIRAL POINCARÉ DUALITY 537 ... Pi} of differential bundles and a differential bundle Q let DiffI({Pi},Q) denote the subspace of the space of maps ⊗ICPi −→ Q which are differential operators by each ...
... algebra U T of a Picard algebroid T is a sheaf of filtered associative algebras over X, cal... more ... algebra U T of a Picard algebroid T is a sheaf of filtered associative algebras over X, called a twisted algebra of differential operators, cf. [BB], 2.1.3. These algebras form a groupoid TDO(X). The functor U defines an equivalence Page 5. Gerbes of chiral differential operators. ...
Each flag manifold carries a unique algebra of chiral differential operators. Continuing along th... more 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.
... Here Lie(V ) denotes the Lie algebra of Fourier components of the fields of V . ... CHIRAL PO... more ... Here Lie(V ) denotes the Lie algebra of Fourier components of the fields of V . ... CHIRAL POINCARÉ DUALITY 537 ... Pi} of differential bundles and a differential bundle Q let DiffI({Pi},Q) denote the subspace of the space of maps ⊗ICPi −→ Q which are differential operators by each ...
... algebra U T of a Picard algebroid T is a sheaf of filtered associative algebras over X, cal... more ... algebra U T of a Picard algebroid T is a sheaf of filtered associative algebras over X, called a twisted algebra of differential operators, cf. [BB], 2.1.3. These algebras form a groupoid TDO(X). The functor U defines an equivalence Page 5. Gerbes of chiral differential operators. ...
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