Charged black holes in the 1/N expansion

Abstract

We study some implications of $SU(N)\times U(1)$ theories coupled to gravity in the large-$N$ limit. We find that in theories with quarks transforming as $q\sim (\mathbf{N},1)$, black holes (BH) with charge larger than a critical value approach extremality $(M_{\rm BH}=\sqrt{2} M_{\rm Pl} Q_{\rm BH})$ as they evaporate. This occurs because BHs in this theory can only lose charge by emitting baryons, a process suppressed by a combinatoric factor $e^{-N\log N}$. Once extremality is reached the BH evolution halts for exponentially long times, $\tau_{\rm BH}\gtrsim e^{N\log N}$, without being protected by any symmetry. At times $t\gg\tau_{\rm BH}$ the BH forms a cloud of deconfined quarks around it, a \textit{quark corona}. The quarks are connected to the horizon by strings extending throughout distances that can be much larger than the inverse of the confinement scale, $\Lambda_N^{-1}$. Strikingly, due to energy conservation, these long strings cannot break even for light quarks. These effects can be further enhanced in clockwork-like theories based on Yang-Mills sectors of the type, $SU(N_1)\times SU(N_2)\times ...\times U(1)$. As an application to phenomenology, we give examples where BHs as light as one gram survive until today without evaporating, opening up regions of parameter space for primordial BH dark matter previously excluded by Hawking evaporation. This result relies only on large-$N$ combinatorics and is independent of the radiation mechanism from the BH, particle masses, and confinement scale. The theories we discuss pass non-trivial tests imposed by Swampland conjectures, including completeness of the spectrum as well as the weak gravity conjecture.