Factorizations of 3d Interval Partition Functions

Abstract

We show that interval partition functions (transition amplitudes) of three- dimensional $\mathcal{N}=2$ theories admit factorizations into sums of products of hemisphere partition functions with Wilson loop insertions glued by suitable factors. We prove the factorization explicitly for supersymmetric quantum electrodynamics and Chern-Simons- Yang-Mills theories. In the former case, we show that the gluing factors can be naturally interpreted in terms of $S^2\times S^1$ partition functions. In the latter case, we prove that hemisphere partition functions are affine characters and determine the gluing factors explicitly in special cases.

published version