  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.

High Energy Physics - Theory