Negative scalar potentials and the swampland: an Anti-Trans-Planckian Censorship Conjecture

Abstract

Abstract 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 ≥ c0 when V′ ≥ 0. The rate $$ {c}_0=2/\sqrt{\left(d-1\right)\left(d-2\right)} $$ c 0 = 2 / d − 1 d − 2 is successfully tested in several string compactifications for d ≥ 4. In addition, a new asymptotic condition, V′′/V ≥ $$ {c}_0^2 $$ c 0 2 , is derived. By extrapolation to anti-de Sitter solutions of radius l, we infer the existence of a scalar whose mass should obey m2l2 ≲ −2. This property is verified in many supersymmetric examples.