What is that hemisphere partition function? Consider a gauged linear sigma model with superpotential, namely a reductive complex Lie group $G$ acting on $V$ preserving volume form and a superpotential $W: V \to \C$. To get $\Z$-graded MF category, we choose certain non-negative $R$-charge (could be in $\Q$) so that $W$ has weight $2$.

We consider the $G \times \R$-equivariant MF, call it $M$. In different GIT chamber, we get different contour deformation $Z(M;t)$.

• anything supported on the unstable loci has $Z=0$
• deep in the GIT chamber, anything converges.