We study 4d N=1 supersymmetric theories on  a compact Euclidean manifole of the form S1xM3. Taking  the limit of shrinking S1, we present a general formula for the limit of the localization integrand, derived by simple effective theory considerations. The limi is given in terms of an effective potential for the holonomies around the S1, whose minima determine the asymptotic behavior of the partition function.