Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus

Understand

We probe the 3d-3d correspondence for mapping cylinder/torus using the superconformal index.

• We focus on the case when the fiber is a once-punctured torus (\Sigma_{1,1}).
• The corresponding 3d field theories can be realized using duality domain wall theories in 4d N=2* theory.
• We show that the superconformal indices of the 3d theories are the SL(2,C) Chern-Simons partition function on the mapping cylinder/torus.