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String Path Integral Realization of Vertex Operator Algebras
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Affine Kac-Moody algebras are natural generalizations of finite-dimensional simple Lie algebras, and they have many important applications, such as the Rogers-Ramanujan identities and soliton equations. The aim of this book is to establish relations between vertex operator algebras in mathematics and the string path integrals of physics. The author realizes representation spaces of vertex operator algebras as spaces of functionals on functions on a circle. Integral kernels of products of vertex operators are interpreted as string path integrals over cylinders. Their traces are interpreted as s...
Affine Kac-Moody algebras are natural generalizations of finite-dimensional simple Lie algebras, and they have many important applications, such as the Rogers-Ramanujan identities and soliton equations. The aim of this book is to establish relations between vertex operator algebras in mathematics and the string path integrals of physics. The author realizes representation spaces of vertex operator algebras as spaces of functionals on functions on a circle. Integral kernels of products of vertex operators are interpreted as string path integrals over cylinders. Their traces are interpreted as string path integrals over elliptic curves. The book provides readers with background in vertex operator algebras and in the basic techniques of string path integrals.
Table of contents:
Vertex operator algebras: Fock spaces; Vertex operators; Representations; Geometric realization of vertex operator algebras; Functional realization of Fock spaces; Function spaces of Reimann surfaces; Geometric realization of vertex operators; Analytic Realization of vertex operator algebras; Zeta-regularization; Zeta-regularized determinants on cylinders and elliptic curves; String path integrals over cylinders and elliptic curves.
Table of contents:
Vertex operator algebras: Fock spaces; Vertex operators; Representations; Geometric realization of vertex operator algebras; Functional realization of Fock spaces; Function spaces of Reimann surfaces; Geometric realization of vertex operators; Analytic Realization of vertex operator algebras; Zeta-regularization; Zeta-regularized determinants on cylinders and elliptic curves; String path integrals over cylinders and elliptic curves.