The Desert and the Swampland

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.

Moduli-dependent species scale

“…For example, for the mirror of the quintic threefold, this leads to the Landau-Ginzburg point as the desert point. We also ask whether this notion of a desert point agrees with the BPS notion defined in [9]. We find that in some cases (such as for the quintic) it does and in some other cases it does not.…”

“…Still, as a starting point instead of Λ EFT one may consider the BPS mass gap, Λ BPS , corresponding to the mass of the lightest BPS state in the spectrum. The behavior of Λ BPS in the interior of moduli space was investigated in [9].…”

“…This general question was studied recently in [9] where the idea pursued was to study the gap in the spectrum of massive states to define an analog of the species scale, i.e. where the first massive state, not part of the EFT, appears.…”

E9 symmetry in the heterotic string on S1 and the weak gravity conjecture

“…Furthermore, an exhaustive scan of these points is also crucial for the question of string universality and whether the string lamppost can cover all viable theories of Quantum Gravity. This has recently been explored in the context of heterotic compactifications [8][9][10][11], F-theory constructions [12][13][14][15] and also from general supergravity and swampland arguments [15][16][17][18]. A subset of special points lie at infinite distances, where the tower of massless modes predicted by the SDC fits very naturally with the idea of a symmetry enhancement.…”

$E_9$ symmetry in the Heterotic String on $S^1$ and the Weak Gravity Conjecture

“…Furthermore, an exhaustive scan of these points is also crucial for the question of string universality and whether the string lamppost can cover all viable theories of Quantum Gravity. This has recently been explored in the context of heterotic compactifications [8][9][10][11], F-theory constructions [12][13][14][15] and also from general supergravity and swampland arguments [15][16][17][18]. A subset of special points lie at infinite distances, where the tower of massless modes predicted by the SDC fits very naturally with the idea of a symmetry enhancement.…”