The web of swampland conjectures and the TCC bound
David Andriot, Niccolò Cribiori, David Erkinger
Abstract
A bstract We consider the swampland distance and de Sitter conjectures, of respective order one parameters λ and c . Inspired by the recent Trans-Planckian Censorship conjecture (TCC), we propose a generalization of the distance conjecture, which bounds λ to be a half of the TCC bound for c , i.e. $$ \lambda \ge \frac{1}{2}\sqrt{\frac{2}{3}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> <mml:mo>≥</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:msqrt> <mml:mfrac> <mml:mn>2</mml:mn> <mml:mn>3</mml:mn> </mml:mfrac> </mml:msqrt> </mml:math> in 4d. In addition, we propose a correspondence between the two conjectures, relating the tower mass m on the one side to the scalar 1 potential V on the other side schematically as $$ m\sim {\left|V\right|}^{\frac{1}{2}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>m</mml:mi> <mml:mo>∼</mml:mo> <mml:msup> <mml:mfenced> <mml:mi>V</mml:mi> </mml:mfenced> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:msup> </mml:math> , in the large distance limit. These proposals suggest a generalization of the scalar weak gravity conjecture, and are supported by a variety of examples. The lower bound on λ is verified explicitly in many cases in the literature. The TCC bound on c is checked as well on ten different no-go theorems, which are worked-out in detail, and V is analysed in the asymptotic limit. In particular, new results on 4d scalar potentials from type II compactifications are obtained.