The Desert and the Swampland

TL;DR

This paper explores the structure of the moduli space in supergravity theories, proposing a bound on light modes to address the black hole species problem and implications for string vacua and moduli stabilization.

Contribution

It introduces the BPS desert conjecture, linking the number of light modes to the species scale and moduli stabilization challenges in string theory.

Findings

The species scale depends more strongly on the number of massless modes in string vacua.

The BPS desert conjecture suggests a bound on the number of light modes to resolve the species problem.

Obstructions to semi-classical moduli stabilization arise for large numbers of moduli.

Abstract

The most natural expectation away from asymptotic limits in moduli space of supergravity theories is the desert scenario, where there are few states between massless fields and the quantum gravity cutoff. In this paper we initiate a systematic study of these regions deep in the moduli space, and use it to place a bound on the number of massless modes by relating it to the black hole species problem. There exists a consistent sub-Planckian UV cutoff (the species scale) which resolves the black hole species problem without bounding the number of light modes. We reevaluate this in the context of supersymmetric string vacua in the desert region and show that even though heuristically the species scale is compatible with expectations, the BPS states of the actual string vacua lead to a stronger dependence of the cutoff scale on the number of massless modes. We propose that this discrepancy, which can be captured by the "BPS desert conjecture", resurrects the idea of a uniform bound on the number of light modes as a way to avoid the black hole species problem. This conjecture also implies a stronger form of the Tadpole Conjecture, which leads to an obstruction in stabilizing all moduli semi-classically for large number of moduli in flux compactifications.