IISER MOHALI

Abstract: Conformal supergravity provides a powerful off-shell framework for analyzing supersymmetric solutions in higher-derivative supergravity theories. This approach was employed by Cardoso et al. (hep-th/0009234) to classify all stationary supersymmetric solutions in higher-derivative N=2 supergravity in four dimensions. Their analysis revealed that both AdS2×S2 and flat space preserve the full N=2 supersymmetry, while extremal black holes preserve only a residual N=1 supersymmetry.
In this talk, we will begin with a brief review of their work and then present our results (arXiv:2505.00638), where we extend the classification to fully supersymmetric solutions in higher-derivative N=3 and N=4 supergravity in four dimensions, again utilizing the conformal supergravity framework. Our findings indicate that, unlike the N=2 case, these extended supergravity theories admit only flat space as a fully supersymmetric solution.

We will also discuss the underlying reasons for the richer structure of supersymmetric vacua in N=2 compared to N=3 and N=4, focusing on key differences in their auxiliary field content and multiplet structure. We will conclude with an overview of our ongoing work aimed at classifying half-BPS and quarter-BPS solutions in N=4 supergravity.