论文标题
二维形成性场理论，完整的顶点代数和电流 - 电流变形
Two-dimensional conformal field theory, full vertex algebra and current-current deformation
论文作者
论文摘要
本文的主要目的是数学构建二维形成式磁场理论的非扰动变形。我们介绍了一个完整的顶点代数的概念，该代数制定了紧凑的二维形式的共形场理论。然后，我们构建了一个完整顶点代数的变形家族，该家族是物理学中保形场理论的当前流动变形。变形的参数空间表示为正交群的双重固定，这是正交司法的商。作为应用程序，我们考虑了手性保形场理论的变形，顶点操作员代数。 “顶点操作员代数”的当前电流变形可能会产生新的顶点操作员代数。我们提供了一个以这种方式获得的顶点算子代数的同构类算子的数量的公式。我们为中央电荷的一些全体形态顶点操作员代数$ 24 $证明了这一点。
The main purpose of this paper is a mathematical construction of a non-perturbative deformation of a two-dimensional conformal field theory. We introduce a notion of a full vertex algebra which formulates a compact two-dimensional conformal field theory. Then, we construct a deformation family of a full vertex algebra which serves as a current-current deformation of conformal field theory in physics. The parameter space of the deformation is expressed as a double coset of an orthogonal group, a quotient of an orthogonal Grassmannian. As an application, we consider a deformation of chiral conformal field theories, vertex operator algebras. A current-current deformation of a "vertex operator algebra" may produce new vertex operator algebras. We give a formula for counting the number of the isomorphic classes of vertex operator algebras obtained in this way. We demonstrate it for some holomorphic vertex operator algebra of central charge $24$.
