2011/07/19 by Liang Kong, Kong, Liang
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.1107.3649
46 pages, a contribution to Mathematical Foundations of Quantum Field and Perturbative String Theory, Hisham Sati, Urs Schreiber (eds.), Proceedings of Symposia in Pure Mathematics, AMS
arxiv created 2011/07/19 · openalex publication_date 2011/07/19 · arxiv updated 2011/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is a review of open-closed rational conformal field theory (CFT) via the theory of vertex operator algebras (VOAs), together with a proposal of a new geometry based on CFTs and D-branes. We will start with an outline of the idea of the new geometry, followed by some philosophical background behind this vision. Then we will review a working definition of CFT slightly modified from Segal's original definition and explain how VOA emerges from it naturally. Next, using the representation theory of rational VOAs, we will discuss a classification result of open-closed rational CFTs, from which some basic properties of a rational CFT, such as the Holographic Principle, can be derived. They will also serve as supporting evidences for the vision of a new geometry. In the end, we briefly discuss the connection between our vision of a new geometry and other topics.