Given a differential operator D with adjoint D†, the index of D is usually defined (mathematically) by
ind D=dimkerD−dimkerD†.
Alternatively, we can talk about the superconformal index
I(βj)=TrH(−1)Fe−γ{Q,Q†}e−∑jβjtj,
where
F is the fermion number,
Q is the supercharge, and
tj's are generators of the Cartan subalgebra of the superconformal and flavor symmetry algebra that commute with
Q. In short, the superconformal index is the Witten index for superconformal field theories in radial quantization. My question is what operator
D is the superconformal index
I(βj) counting? Is it the supercharge operator
Q? Or is it a different operator?