Topologizations of Chiral Representations
Florian Conrady (Heidelberg U. & Potsdam, Max Planck Inst.), Christoph, Schweigert (Paris U., VI-VII & Aachen, Tech. Hochschul.)
TL;DR
This paper compares two topologies proposed for chiral algebra representations, showing one is coarser and proving the continuity of two-point blocks in Huang's topology, advancing the mathematical understanding of chiral conformal field theories.
Contribution
It provides a detailed comparison of Huang's and Gaberdiel & Goddard's topologies and establishes the continuity of chiral two-point blocks in Huang's topology.
Findings
Gaberdiel & Goddard's topology is coarser for suitable pairs
Chiral two-point blocks are continuous in Huang's topology
New proof of continuity enhances mathematical foundations
Abstract
We analyze and compare two families of topologies that have been proposed for representation spaces of chiral algebras by Huang and Gaberdiel & Goddard respectively. We show, in particular, that for suitable pairs the topology of Gaberdiel & Goddard is coarser. We also give a new proof that the chiral two-point blocks are continuous in the topology of Huang.
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