Partition Functions of Chern-Simons Theory on Handlebodies by Radial Quantization

Understand

We use radial quantization to compute Chern-Simons partition functions on handlebodies of arbitrary genus.

• The partition function is given by a particular transition amplitude between two states which are defined on the Riemann surfaces that define the (singular) foliation of the handlebody.
• The final state is a coherent state while on the initial state the holonomy operator has zero eigenvalue.
• The latter choice encodes the constraint that the gauge fields must be regular everywhere inside the handlebody.