Entropy Bounds and the Species Scale Distance Conjecture

TL;DR

This paper derives bounds on the rate at which the species scale decreases near infinite distance points in moduli space, using entropy bounds, and introduces the Species Scale Distance Conjecture (SSDC) as a universal principle.

Contribution

It provides a bottom-up derivation of the SDC features using the Covariant Entropy Bound and proposes the SSDC as a universal convex hull condition on the species scale decay rate.

Findings

Recovered key features of the SDC from entropy considerations.

Proposed universal bounds on the species scale decay rate.

Verified the SSDC in M-theory toroidal compactifications.

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 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 $\lambda_{\text{sp}}$ 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 (asymptotic) 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.