Factorising the 3D topologically twisted index

We explore the path integration — upon the contour of hermitian (non-auxliary) field configurations — of topologically twisted N=2 Chern-Simons-matter theory (TTCSM) on S₂ times a segment. In this way, we obtain the formula for the 3D topologically twisted index, first as a convolution of TTCSM on S₂ times halves of S₁, second as TTCSM on S₂ times S₁ — with a puncture, — and third as TTCSM on S₂×S₁. In contradistinction to the first two cases, in the third case, the vector multiplet auxiliary field D is constrained to be anti-hermitian.