Black hole microstates and supersymmetric localization

Understand

This thesis focuses mainly on understanding the origin of the Bekenstein-Hawking entropy for a class of four- and five-dimensional BPS black holes in string/M-theory.

• To this aim, important ingredients are holography and supersymmetric localization.
• Using the method of supersymmetric localization, the Euclidean path integrals for supersymmetric field theories on $\Sigma_\mathfrak{g} \times T^{n}$ $(n=1,2)$, with at least four real supercharges, can be reduced to a matrix integral that depends on background magnetic fluxes and chemical potentials for the global symmetries of the theory.
• This defines the topologically twisted index which, upon extremization with respect to the chemical potentials, is conjectured to reproduce the entropy of magnetically charged static BPS AdS$_{4/5}$ black holes/strings.