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Level N Teichm\"uller TQFT and Complex Chern-Simons Theory

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arxiv 1612.06986 v1 pith:7ZIXL5HN submitted 2016-12-21 math.GT math.QA

J{o}rgen Ellegaard Andersen , Simone Marzioni This is my paper · ORCID
classification math.GTmath.QA
keywords theorylevelteichmtqftchern--simonschern-simonscomplexconstruction
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abstract

In this manuscript we review the construction of the Teichm\"{u}ller TQFT in [AK1], upgrading it to a theory dependent on an extra odd integer $N$ using results developed in [AK3]. We also describe how this theory is related with quantum Chern--Simons Theory at level $N$ with gauge group $\rm{PSL}(2,\mathbb{C})$.

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  1. Hamiltonian quantization of complex Chern-Simons theory at level-$k$

    hep-th 2025-04 conditional novelty 6.0 of 10

    The physical Hilbert space of complex Chern-Simons theory on an m-holed sphere at even level carries a Fenchel-Nielsen representation in which Wilson loops along pants-decomposition cuts act as multiplication operators.

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