Cardy Formulae for SUSY Theories in d=4 and d=6

Understand

We consider supersymmetric theories on a space with compact space-like slices.

• One can count BPS representations weighted by (-1)^F, or, equivalently, study supersymmetric partition functions by compactifying the time direction.
• A special case of this general construction corresponds to the counting of short representations of the superconformal group.
• We show that in four-dimensional N=1 theories the "high temperature" asymptotics of such counting problems is fixed by the anomalies of the theory.