  For Chern-Simons-matter theories in three dimensions, gauge invariance may
require the Chern-Simons level k to be half-integral, in which case parity is
violated. As noted by Pasquetti for abelian theories with N=2 supersymmetry,
the partition function on the ellipsoid also admits a suitable holomorphic
factorization precisely when the value of k is properly quantized. Using known
formulas for the partition function, we investigate analytic aspects of this
factorization for non-abelian gauge groups and general matter representations.
We verify that factorization occurs in accord with the parity anomaly for the
classical matrix groups and for the exceptional group G_2. In an appendix, we
discuss the analytic continuation of torus knot observables in the SU(2)
Chern-Simons-matter theory.
