Factorisation of N=2 theories on the squashed 3-sphere

Partition functions of N = 2 theories on the squashed 3-sphere have been recently shown to localise to matrix integrals. By explicitly evaluating the matrix integral we show that abelian partition functions can be expressed as a sum of products of two blocks. We identify the first block with the partition function of the vortex theory, with equivariant parameter (sic) = 2 pi ib(2), defined on R-2 x S-1 corresponding to the b -> 0 degeneration of the ellipsoid. The second block gives the partition function of the vortex theory, with equivariant parameter (sic)(L) = 2 pi i/b(2), on the dual R-2 x S-1 corresponding to the 1/b -> 0 degeneration. The ellipsoid partition appears to provide the (sic) -> (sic)(L) modular invariant non-perturbative completion of the vortex theory.