Charged black holes in the 1/N expansion

TL;DR

This work shows that SU(N)×U(1) gauge theories coupled to gravity at large N admit charged black holes that inexorably approach extremality due to combinatorial suppression of charged emission. Above a critical charge, BHs become exponentially long-lived, and when a corona forms, deconfined quarks remain bound by strings extending far from the horizon, preventing string breaking. The authors derive static corona solutions, analyze the dynamics and validity of the dilute-string-gas regime, and discuss swampland constraints, including spectrum completeness and the weak gravity conjecture. They propose phenomenological consequences, notably the possibility of ultralight primordial BH dark matter stabilized by large-N effects, and outline clockwork-like extensions to realize very large effective N in hidden sectors. Overall, the paper highlights a novel interplay between large-N confinement, gravity, and BH evolution with potential cosmological and observational implications.

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, $τ_{\rm BH}\gtrsim e^{N\log N}$, without being protected by any symmetry. At times $t\ggτ_{\rm BH}$ 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, $Λ_N^{-1}$. 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.

Figures (2)

• Figure 1: Two different configurations with strings of different lengths used to compare their (free) energy. The top one corresponds to unbroken long strings with energy $\mathcal{E}_1$. The bottom is a configuration after nucleating a $q\bar{q}$ pair on the flux. This configuration has energy $\mathcal{E}_2$. As discussed in the main text, we always have $\mathcal{E}_2 > \mathcal{E}_1$ and the breaking of flux tubes by quark nucleation is energetically forbidden.
• Figure 2: Qualitative evolution of large-$N$ black holes. The shaded blue region corresponds to BH solutions without a corona due to their small electric field near the horizon, $eE< \Lambda_N^2$. The shaded green corresponds to BH solutions with electric field $eE>\Lambda_N^2$ for which the formation of a quark corona is possible. The line $Q_{\rm BH} = \sqrt{2}M_{\rm BH}/M_{\rm Pl}$ corresponds to BH extremality condition which separates the previous regions from the super-extremal region (in shaded red), forbidden by cosmic censorship. The black dots correspond to sub-extremal BH solutions with initial mass and charge such that $eE\ll \Lambda_N^2$. As these BH have $Q_{\rm BH}> Q_{\rm crit}$, we note that their evolution is such that $\dot{M}_{\rm BH}\gg \dot{Q}_{\rm BH}\approx 0$ and they always flow to extremality. After reaching extremality, they track the extremal line and reach the yellow point, $(M_{\rm crit},Q_{\rm crit})$, which becomes an attractor (see section \ref{['sec:dynamics']}). After this, the BHs populate a quark corona and evolve near extremality until the charge in the corona becomes $Q_{\rm cor}=\frac{1}{e}\frac{Q_{\rm BH}^2}{Q_{\rm crit}}$. As the baryon emission is exponentially suppressed, we can solve for the BH charge and obtain the charge below which string-string interactions become important, $Q_{\rm int}\approx e^{3/2}\frac{M_{\rm Pl}^2}{\Lambda_N^2}$. Below this charge our qualitative description of a near-extremal BH breaks down.