Superconformal index of higher derivative $\mathcal N=1$ multiplets in four dimensions

Understand

Supersymmetric partition function of $\mathcal N=1$ superconformal theories on $S^1_{\beta} \times S^3$ is related to the superconformal index receiving contributions from short representations.

• The leading coefficients in the small $\beta$ (high "temperature") expansion of the index were previously related to the conformal anomaly coefficients of the theory.
• Assumptions underlying universality of these relations were tested only for simplest low-spin unitary multiplets.
• Here we consider examples of higher derivative non-unitary $\mathcal N=1$ multiplets that naturally appear in the context of extended conformal supergravities and compute their superconformal index.