Entropy bounds and the species scale distance conjecture

Abstract

The Swampland Distance Conjecture (SDC) states that, as we move towards an infinite distance point in moduli space, a tower of states becomes exponentially light with the geodesic distance in any consistent theory of Quantum Gravity. Although this fact has been tested in large sets of examples, it is fair to say that a bottom-up justification based on fundamental Quantum Gravity principles that explains both the geodesic requirement and the exponential behavior has been missing so far. In the present paper we address this issue by making use of the Covariant Entropy Bound as applied to the EFT. When applied to backgrounds of the Dynamical Cobordism type in theories with a moduli space, we are able to recover these main features of the SDC. Moreover, this naturally leads to universal lower and upper bounds on the ‘decay rate’ parameter λsp of the species scale, that we propose as a convex hull condition under the name of Species Scale Distance Conjecture (SSDC). This is in contrast to already proposed universal bounds, that apply to the SDC parameter of the lightest tower. We also extend the analysis to the case in which asymptotically exponential potentials are present, finding a nice interplay with the asymptotic de Sitter conjecture. To test the SSDC, we study the convex hull that encodes the large-moduli dependence of the species scale. In this way, we show that the SSDC is the strongest bound on the species scale exponential rate which is preserved under dimensional reduction and we verify it in M-theory toroidal compactifications.

Stringy evidence for a universal pattern at infinite distance

“…Furthermore, we can also recover the recently proposed lower bound for the exponential rate of the species scale (named the Species Scale Distance Conjecture [43]),…”

“…Notice, though, that these convex hulls can only be defined if there is a region of moduli space in which the hull of the scalar charge-to-mass vectors does not change. In such a case, it follows from (2.6) that both polytopes are dual to each other, as hinted in [43]. This implies, in particular, that given any one of them one can simply retrieve the other upon imposing the aforementioned relation as JHEP06(2024)037 a constraint.…”

“…Since the towers become massless asymptotically, the species scale will also vanish in the infinite distance limit, but this typically happens at a different rate than that of the towers. Analogously, following [43], we can define the Z-vectors as follows…”

“…Sometimes, it gets useful to define the convex hull of the ζ-vectors of all light towers in a given asymptotic regime [25], since this provides us information about which tower is dominating along each direction. Analogously, one can define the convex hull of Z-vectors of the species scale as in [43], thus informing us about the nature of the infinite distance limit, namely the quantum gravity theory above Λ sp . Notice, though, that these convex hulls can only be defined if there is a region of moduli space in which the hull of the scalar charge-to-mass vectors does not change.…”

Global anomalies & bordism of non-supersymmetric strings

“…Despite this, recent research in this direction has yielded e.g. metastable vacua [147,169], novel end-of-the-world defects [170][171][172][173][174][175][176], and checks of Swampland constraints [12,20,177]. The results that we have presented in this paper are yet another step in this direction.…”