Factorizations of 3d interval partition functions

A bstract We show that interval partition functions (transition amplitudes) of three-dimensional $$ \mathcal{N} $$ 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 × 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.