bibkey: grootnibbelink2020tension authors: Stefan Groot Nibbelink; Orestis Loukas; Andreas Mütter; Erik Parr; Patrick K. S. Vaudrevange year: 2020 title: “Tension between a vanishing cosmological constant and non-supersymmetric heterotic orbifolds” doi: 10.1002/prop.202000044 url: https://arxiv.org/abs/1710.09237v1 claim: “There does not exist any finite group H that has a four-dimensional representation D_4 with (i) det(D_4(h)) = 1 for all h in H, (ii) no trivial singlet of H, (iii) but whose branchings to all Z_N subgroups of H always contain the trivial Z_N-singlet (Conjecture, checked for the 1,594 CARAT groups and all groups of order at most 500).” strata_touched:

• D5/S3/Quantum/Algebra/FourDimensionalSingletBranching license: citation-only triage: anchor

Tension between a vanishing cosmological constant and non-supersymmetric heterotic orbifolds

S. Groot Nibbelink, O. Loukas, A. Mütter, E. Parr and P. K. S. Vaudrevange, arXiv:1710.09237 (v1 2017-10-25, the only version); Fortschr. Phys. 68 (2020) 2000044. Subject: hep-th.

The paper studies heterotic orbifolds in which every twisted sector is locally supersymmetric while no gravitino survives globally, as a route to a vanishing one-loop cosmological constant. Local Killing spinors are counted by trivial singlets in the branching of the spinor representation 4 of the point group to its cyclic subgroups, and global ones by trivial singlets of the whole group. In the subsection “A Finite Group Conjecture” the paper states:

There does not exist any finite group $\mathbf{H}$ that has a
four-dimensional representation $D_\rep{4}$ with the following three
properties: (i) $D_\rep{4}$ has a trivial determinant, i.e.
$\det\left(D_\rep{4}(\gth)\right) = 1$ for all $\gth \in \mathbf{H}$, (ii)
$D_\rep{4}$ does not contain the trivial singlet representation of
$\mathbf{H}$, (iii) but the branchings of $D_\rep{4}$ to all $\Z{N} \subset
\mathbf{H}$ subgroups always contain the trivial $\Z{N}$-singlet
representation.

It is checked by computer for the 1,594 finite groups from the CARAT ℚ-classes and all finite groups of order at most 500, and it fails for five-dimensional representations (a Q₈ example).

Verified locator

• DOI: https://doi.org/10.1002/prop.202000044 (the journal text was not read).
• URL: https://arxiv.org/abs/1710.09237v1 (source retrieved 2026-09-30): subsection “A Finite Group Conjecture” (the conjecture and its computer checks) and the conclusion (“a future direction for mathematical work could be to either prove this conjecture or to determine finite groups where it fails”).