Open Verlinde line operators
Davide Gaiotto
TL;DR
This paper introduces a reformulation of Verlinde line operators using 3D topological field theory, extending their application to open paths on Riemann surfaces and exploring implications for quantum theories.
Contribution
It presents a novel 3D TFT formulation of open Verlinde line operators, expanding their scope beyond closed loops and linking to various quantum mathematical and physical theories.
Findings
Extended Verlinde line operators to open paths on Riemann surfaces
Connected open Verlinde operators to quantum Teichmüller theory and quantum groups
Provided a new framework for analyzing line operators in conformal field theory
Abstract
We reformulate the action of Verlinde line operators on conformal blocks in a 3d TFT language and extend it to line operators labelled by open paths joining punctures on the Riemann surface. We discuss the possible applications of open Verlinde line operators to quantum Teichm\"uller theory, supersymmetric gauge theory and quantum groups
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic structures and combinatorial models · Advanced Operator Algebra Research