The genus one Complex Quantum Chern-Simons representation of the Mapping Class Group
J{\o}rgen Ellegaard Andersen, Simone Marzioni
TL;DR
This paper explicitly computes the genus one quantum representation of the mapping class group in complex quantum Chern-Simons theory for any simple, simply connected complex gauge group, using a generalized Weil-Gel'fand-Zak transform.
Contribution
It provides an explicit formula for the genus one quantum representation of the mapping class group in complex quantum Chern-Simons theory, extending previous theoretical frameworks.
Findings
Explicit expression for the representation derived
Generalization of Weil-Gel'fand-Zak transform used
Applicable to any simple, simply connected complex gauge group
Abstract
In this paper we compute explicitly, following Witten's prescription, the quantum representation of the mapping class group in genus one for complex quantum Chern-Simons theory associated to any simple and simply connected complex gauge group . We use a generalization of the Weil-Gel'fand-Zak transform to exhibit an explicit expression for the representation.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Black Holes and Theoretical Physics · Algebraic structures and combinatorial models