Deformations of Geometric Structures inTopological Sigma Models

摘要

We study a Lie algebra of formal vector fields W_n with it application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. We show that equivalent classes of deformations are described by a Hochschild cohomology of the DG-algebra 2l = (A, Q), Q = θ + θ_(deform), which is defined to be the cohomology of (-1)~nQ+ d_(Hoch). Here θ is the initial non-deformed BRST operator while θ_(deform) is the deformed part whose algebra is a Lie algebra of linear vector fields gl_n.