I will consider 4d =1 supersymmetric theories on a compact Euclidean manifold of the form S1×3. Taking the limit of shrinking S1, I will present a general formula for the limit of the localization integrand, derived by simple effective theory considerations. The limit is given in terms of an effective potential for the holonomies around the S1, whose minima determine the asymptotic behavior of the partition function. If the potential is minimized in the origin, where it vanishes, the partition function has a Cardy-like behavior fixed by Tr(R), while a nontrivial minimum gives a shift in the coefficient. I will also discuss the generalization to 6d N=(1,0) indices and an application to Schur indices.
Brown Bag Seminars >