3d Partition Function as Overlap of Wavefunctions

Understand

We compute the partition function on S^3 of 3d N=4 theories which arise as the low-energy limit of 4d N=4 super Yang-Mills theory on a segment or on a junction, and propose its 1d interpretation.

• We show that the partition function can be written as an overlap of wavefunctions determined by the boundary conditions.
• We also comment on the connection of our results with the 4d superconformal index and the 2d q-deformed Yang-Mills theory.