Witten's Dark Fantasy




String theory



What has been called Witten’s dark fantasy in Heckmann-Lawrie-Lin-Zoccarato 19, Section 8 is an argument, going back to Witten 95a, Witten 95b, Sec. 3, Witten 00, p. 7 for the existence of non-perturbative non-supersymmetric 4d string vacua/string phenomenology with fundamentally vanishing cosmological constant (“dark energy”).

The original idea was formulated in terms of 3d M-theory on 8-manifolds decompactified at strong coupling to 4d via duality between M-theory and type IIA string theory (recall the super 2-brane in 4d).

Based on the observation of Vafa 96, Section 4.3 that the argument should have a natural realization in 4d F-theory on Spin(7)-manifolds (T-dual to the previous perspective), a detailed construction was finally laid out in Bonetti-Grimm-Pugh 13, Heckmann-Lawrie-Lin-Zoccarato1 18, Heckman-Lawrie-Lin-Sakstein-Zoccarato 19.


The key technical point is the claim that a careful analysis of D=4 N=1 supergravity obtained after KK-compactification of F-theory on Spin(7)-manifolds T-dual to M-theory on Spin(7)-manifolds reveals, in contrast to the N=1 supersymmetry of F-theory on CY4-folds, an “N=1/2N= 1/2 supersymmetry” where

  1. the vacuum state is supersymmetric and hence has vanishing cosmological constant;

  2. but no finite-energy-excitation of the vacuum appears supersymmetrically,

    hence fermions and bosons in the model do not appear in supersymmetric spectra.

(Vafa 96, Sec. 4.3 BGP 13, HLLZ 18, Sec. 4)

History and phenomenological context

When the idea was proposed in Witten 95a, Witten 95b, Witten 00 it was right before observation of red shifts of supernovae convinced cosmologists, in 2001, of a relatively small but positive cosmological constant. When this result became enshrined in what is now the standard model of cosmology the idea of vanishing cosmological constant in string theory fell out of favor, and a vocal sub-community instead embarked on arguing that de Sitter spacetime-string vacua with positive cosmological constant had to be searched at random in a large landscape of string theory vacua.

However, debate remains that the apparently observed cosmological constant is but an artefact of the usual FRW model-cosmologies not taking sizeable backreaction of cosmic inhomogeneities into account. The situation with this debate currently remains open (see at inhomogeneous cosmology). In the extreme case, if cosmic inhomogeneity, possibly combined with higher curvature corrections to gravity (such as control the observationally preferred Starobinsky model of cosmic inflation), would explain all of the apparently observed cosmological constant, then Witten’s dark fantasy would again appear to be viable string phenomenology.


The idea in rough form goes back to

The observation that the idea should naturally embed in F-theory, namely as F-theory on Spin(7)-manifolds is due to

A detailed implementation of the idea in F-theory on Spin(7)-manifolds is developed in:

Last revised on November 21, 2019 at 03:45:11. See the history of this page for a list of all contributions to it.