论文标题
完整顶点代数和自举 - 2D CFT中四个点功能的一致性
Full vertex algebra and bootstrap -- consistency of four point functions in 2d CFT
论文作者
论文摘要
在物理学中，据信，二维形成式磁场理论的一致性遵循引导方程。在本文中，我们通过分析Bootstrap方程来介绍完整顶点代数的概念，这是$ \ Mathbb {Z} $ - 分级顶点代数的“真实分析”概括。我们还提供了在二维形式的保形场理论中对四个点相关函数的一致性的数学表述，并证明了它的完整顶点代数，并具有对形式对称性的其他假设。特别是，我们表明，引导程序方程与共形对称性意味着四个点相关函数的一致性。作为一种应用，构建了由格拉马尼亚人参数的完整顶点代数的可变形家族，它出现在字符串理论的环形紧凑型中。这为我们提供了满足上述假设的例子。
In physics, it is believed that the consistency of two dimensional conformal field theory follows from the bootstrap equation. In this paper, we introduce the notion of a full vertex algebra by analyzing the bootstrap equation, which is a "real analytic" generalization of a $\mathbb{Z}$-graded vertex algebra. We also give a mathematical formulation of the consistency of four point correlation functions in two dimensional conformal field theory and prove it for a full vertex algebra with additional assumptions on the conformal symmetry. In particular, we show that the bootstrap equation together with the conformal symmetry implies the consistency of four point correlation functions. As an application, a deformable family of full vertex algebras parametrized by the Grassmanian is constructed, which appears in the toroidal compactification of string theory. This give us examples satisfying the above assumptions.
