The role of supersymmetry in near-extremal black hole thermodynamics

In this work we study the effective Schwarzian theories arising in the description of near-extremal and near-BPS black holes in 4d, N=2 ungauged supergravity. The supergravity models we consider are such that the supersymmetry of the extremal solutions can be either preserved or broken by flipping the sign of some of the charges. We obtain the Schwarzian in two ways: by studying the (super)isometries of the extremal solutions and by performing the dimensional reduction to 2d of both the bosonic and fermionic sectors in the 4d supergravity. We then quantize exactly these generalized Schwarzian theories and extract the spectra. When supersymmetry is preserved, the spectrum has a degenerate ground state and a mass gap, in accordance with the semiclassical analysis. When supersymmetry is broken, the spectrum is continuous and has no extremal degeneracy, due to strong quantum effects modifying the Bekenstein-Hawking area law. The 2d gravitinos set apart the dynamics in the two cases, becoming respectively massless and massive.