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After reviewing the role of the twisted index in the microscopic derivation of BH entropy for BPS black holes in AdS4, we will discuss a recent result that aims at reproducing the microscopic entropy of BPS black holes in AdS5 from the dual N=4 SYM theory. This proposal relies on the extremization procedure of a Casimir Energy-like quantity that correctly reproduces the entropy but shows some conflict with constraints from N=4 SYM.
Based on arXiv:1705.05383