扰动Beta-Gamma系统与复几何
Perturbed Beta-Gamma Systems and Complex Geometry
摘要：
我们考虑的方程，所产生的共形不变性条件的扰动弯曲β-γ系统。这些方程具有埃尔米特流形上的爱因斯坦方程的物理意义，其中B场2-形式是虚的，与埃尔米特度量的标准形成比例。我们表明，他们分解成线性和双线性方程，并导致消失的第一陈类的流形系统的定义。我们讨论了这些方程与BRST算子的广义Maurer-Cartan结构的关系。最后我们描述了广义Maurer-Cartan双线性运算与Courant/Dorfman括号的关系。
英文摘要：
We consider the equations, arising as the conformal invariance conditions of the perturbed curved beta-gamma system. These equations have the physical meaning of Einstein equations with a B-field and a dilaton on a hermitian manifold, where the B-field 2-form is imaginary and proportional to the canonical form associated with hermitian metric. We show that they decompose into linear and bilinear equations and lead to the vanishing of the first Chern class of the manifold where the system is defined. We discuss the relation of these equations to the generalized Maurer-Cartan structures related to BRST operator. Finally we describe the relations of the generalized Maurer-Cartan bilinear operation and the Courant/Dorfman brackets.
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