Riemann surfaces with boundaries and the theory of vertex operator algebras
نویسنده
چکیده
The connection between Riemann surfaces with boundaries and the theory of vertex operator algebras is discussed in the framework of conformal field theories defined by Kontsevich and Segal and in the framework of their generalizations in open string theory and boundary conformal field theory. We present some results, problems, conjectures, their conceptual implications and meanings in a program to construct these theories from representations of vertex operator alge-
منابع مشابه
5 A ug 1 99 8 A functional - analytic theory of vertex ( operator ) algebras , I
This paper is the first in a series of papers developing a functionalanalytic theory of vertex (operator) algebras and their representations. For an arbitrary Z-graded finitely-generated vertex algebra (V, Y,1) satisfying the standard grading-restriction axioms, a locally convex topological completion H of V is constructed. By the geometric interpretation of vertex (operator) algebras, there is...
متن کاملA supergeometric interpretation of vertex operator superalgebras
Conformal field theory (or more specifically, string theory) and related theories (cf. [BPZ], [FS], [V], and [S]) are the most promising attempts at developing a physical theory that combines all fundamental interactions of particles, including gravity. The geometry of this theory extends the use of Feynman diagrams, describing the interactions of point particles whose propagation in time sweep...
متن کاملA Complex Structure on the Moduli Space of Rigged Riemann Surfaces
The study of Riemann surfaces with parametrized boundary components was initiated in conformal field theory (CFT). Motivated by general principles from Teichmüller theory, and applications to the construction of CFT from vertex operator algebras, we generalize the parametrizations to quasisymmetric maps. For a precise mathematical definition of CFT (in the sense of G. Segal), it is necessary th...
متن کاملSemi-infinite forms and topological vertex operator algebras
Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial suboperad of the partial operad for semi-infinite forms, topological vertex partial operads of type k < 0 and strong topological vertex partial operads of type k ...
متن کامل0 A functional - analytic theory of vertex ( operator ) algebras , II
For a finitely-generated vertex operator algebra V of central charge c ∈ C, a locally convex topological completion HV is constructed. We construct on HV a structure of an algebra over the operad of the c 2 -th power Det c/2 of the determinant line bundle Det over the moduli space of genus-zero Riemann surfaces with ordered analytically parametrized boundary components. In particular, HV is a m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002