Spin Chern-Simons and Spin TQFTs

Abstract

In a previous paper we constructed classical spin Chern-Simons for any compact Lie group $G$: a gauge theory whose action depends on the spin structure of the 3-manifold. Here we apply geometric quantization to the classical Hamiltonian theory and investigate the formal properties of the partition function in the Lagrangian theory, all in the case $G=S{O}_3$. We find that the quantum theory for $S{O}_3$ spin Chern-Simons corresponds to the spin TQFT constructed by Blanchet and Masbaum in the same way that the quantum theory for standard $S{U}_2$ Chern-Simons corresponds to the TQFT constructed by Reshetikhen and Turaev or the TQFT constructed by Blanchet, Habegger, Masbaum, and Vogel.

References in corpus (1)

• Classical Chern-Simons on manifolds with spin structure