Black holes as probes of moduli space geometry

Abstract

We argue that supersymmetric BPS states can act as efficient finite energy probes of the moduli space geometry thanks to the attractor mechanism. We focus on 4d $$ \mathcal{N} $$ N = 2 compactifications and capture aspects of the effective field theory near the attractor values in terms of physical quantities far away in moduli space. Furthermore, we illustrate how the standard distance in moduli space can be related asymptotically to the black hole mass. We also compute a measure of the resolution with which BPS black holes of a given mass can distinguish far away points in the moduli space. The black hole probes may lead to a deeper understanding of the Swampland constraints on the geometry of the moduli space.

Species entropy and thermodynamics

“…In particular, it was emphasized that the species scale should be a function of the scalar fields and, in the context of compactifications of type II string theory on Calabi-Yau threefolds, such function is related to the topological free energy [24], as it can be also shown from deriving the species entropy as minimal black hole entropy [26]. Moreover, swampland distance relations for the species scale as function of the moduli were recently discussed in [29], while large and small black hole entropy limits and their relations to swampland distance conjectures were recently discussed in the literature [32][33][34]. In our present work, we will see that the swampland bound on the species scale implies analogous bounds on the black hole and species entropies.…”

“…In the following, we provide an algorithm to determine the size of the smallest possible black hole that can be described within effective theory. Since we will work mainly with examples from string theory, this algorithm will be applicable to charged black holes and it will be built on recent works [26,[32][33][34]]. An alternative strategy, valid for Schwarzschild black holes, will be provided in [39] in the context of the N-portrait picture [14], where the smallest possible black hole will have a number of constituents N such that N = S sp .…”

On the correspondence between black holes, domain walls and fluxes

“…At this point, this seems to us a challenging task, whose difficulty is probably related to the fact that such conjectures are not as physically motivated as the distance conjectures that we are going to analyze next. 6…”

“…These ideas are part of broader program, which goes under the name of Swampland Program (see e.g. [1][2][3] for reviews), and they have put black holes under scrutiny: by requiring a consistent description of black hole dynamics in the low energy, one can derive nontrivial properties of the EFT and its breakdown [4][5][6][7]. Moreover, it is a fact that various swampland conjectures can be related and motivated in the context of black holes, see e.g.…”

Cosmic acceleration and turns in the Swampland

“…It should be noted that the most common strategy to construct an effective (supergravity) model is to stabilize all fields except one, which drives the acceleration phase. However, despite its simplicity, this approach may not be the most natural and often demands precise control over the effective theory.3 It has also been pointed out that the limits of small (AdS) cosmological constant[41], small gravitino mass[42][43][44] and small/large entropy[45][46][47][48] lead to analogous conclusions 4. In the context of inflationary cosmology, it has been shown[57][58][59][60][61][62] that non-compact symmetries and negative curvature of the field space are key features for an excellent fit to the observational data.…”