Let M be a Riemannian manifold.For p∈M,the tensor algebra T(T_(p)M_)of the negative part of the affinization T_(p)M of the tangent space T_(p)M of M at p has a natural structure of a meromorphic open-string vertex al...Let M be a Riemannian manifold.For p∈M,the tensor algebra T(T_(p)M_)of the negative part of the affinization T_(p)M of the tangent space T_(p)M of M at p has a natural structure of a meromorphic open-string vertex algebra.These meromorphic open-string vertex algebras form a vector bundle over M with a connection.The author constructs a sheaf V of meromorphic open-string vertex algebras on the sheaf of parallel sections of this vector bundle.Using covariant derivatives,he constructs a representation on the space of smooth functions of the algebra of parallel tensor fields.These representations are used to construct a sheaf W of left V-modules generated by the sheaf of smooth functions.In particular,the author obtains a meromorphic open-string vertex algebra V_(M) as the global sections on M of the sheaf V and a left V_(M)-module W_(M) as the global sections on M of the sheaf W.He shows that the Laplacian on M is in fact a component of a vertex operator for the left V_(M)-module W_(M) restricted to the space of smooth functions.展开更多
基金supported by the National Science Foundation Grant(No.PHY-0901237).
文摘Let M be a Riemannian manifold.For p∈M,the tensor algebra T(T_(p)M_)of the negative part of the affinization T_(p)M of the tangent space T_(p)M of M at p has a natural structure of a meromorphic open-string vertex algebra.These meromorphic open-string vertex algebras form a vector bundle over M with a connection.The author constructs a sheaf V of meromorphic open-string vertex algebras on the sheaf of parallel sections of this vector bundle.Using covariant derivatives,he constructs a representation on the space of smooth functions of the algebra of parallel tensor fields.These representations are used to construct a sheaf W of left V-modules generated by the sheaf of smooth functions.In particular,the author obtains a meromorphic open-string vertex algebra V_(M) as the global sections on M of the sheaf V and a left V_(M)-module W_(M) as the global sections on M of the sheaf W.He shows that the Laplacian on M is in fact a component of a vertex operator for the left V_(M)-module W_(M) restricted to the space of smooth functions.
