Semiclassical Analysis of the 3d/3d Relation

Understand

We provide quantitative evidence for our previous conjecture which states an equivalence of the partition function of a 3d N=2 gauge theory on a duality wall and that of the SL(2,R) Chern-Simons theory on a mapping torus, for a class of examples associated with once-punctured torus.

• In particular, we demonstrate that a limit of the 3d N=2 partition function reproduces the hyperbolic volume and the Chern-Simons invariant of the mapping torus.
• This is shown by analyzing the classical limit of the trace of an element of the mapping class group in the Hilbert space of the quantum Teichmuller theory.
• We also show that the subleading correction to the partition function reproduces the Reidemeister torsion.