Negative scalar potentials and the swampland: an Anti-Trans-Planckian Censorship Conjecture
David Andriot, Ludwig Horer, George Tringas
Abstract
A bstract In this paper, we derive a characterisation of negative scalar potentials, V < 0, in d -dimensional effective theories of quantum gravity. This is achieved thanks to an Anti-Trans-Planckian Censorship Conjecture (ATCC), inspired by a refined version of the TCC. The ATCC relies on the fact that in a contracting universe, modes that become sub-Planckian in length violate the validity of the effective theory. In the asymptotics of field space, we deduce that − V ′ /V ≥ c 0 when V ′ ≥ 0. The rate $$ {c}_0=2/\sqrt{\left(d-1\right)\left(d-2\right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>c</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>/</mml:mo> <mml:msqrt> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> <mml:mfenced> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:msqrt> </mml:math> is successfully tested in several string compactifications for d ≥ 4. In addition, a new asymptotic condition, V ′′ /V ≥ $$ {c}_0^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mn>0</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> , is derived. By extrapolation to anti-de Sitter solutions of radius l , we infer the existence of a scalar whose mass should obey m 2 l 2 ≲ −2. This property is verified in many supersymmetric examples.