The talk will present progress towards a microscopic understanding of the entropy of rotating BPS black holes in AdS. I will describe a new BPS limit of black hole thermodynamics which first focuses on a supersymmetric family of complexified solutions and then reaches extremality. In this limit the chemical potentials obey a constraint that is interpreted as a regularity condition in the...
Based on Nielsen’s geometric approach, the variation of holographic complexity for two nearby target states only depends on the end point of the optimal trajectory, a result designated as the first law of complexity. As an example, we will examine the complexity=action conjecture when the AdS vacuum is perturbed by a scalar field excitation, which corresponds to a coherent state.
