We present a first study of the field spectrum on a class of negatively-curved compact spaces: nilmanifolds or twisted tori. This is a case where analytical results can be obtained, allowing to check numerical methods. We focus on the Kaluza-Klein expansion of a scalar field. The results are then applied to a toy model where a natural Dark Matter candidate arises as a stable massive state of the bulk scalar.

In this letter, we present LHC limits on the minimal universal extra dimension (MUED) model from LHC Run 1 data and current limits from searches of the ongoing Run 2. Typical collider signals of the Kaluza-Klein (KK) states mimic generic degenerate supersymmetry (SUSY) missing transverse momentum signatures since the KK particles cascade decay into jets, leptons and the lightest KK particle which is stable due to KK parity and evades detection. We test the parameter space against a large number of supersymmetry based missing energy searches implemented in the public code CheckMATE. We demonstrate the complementarity of employing various searches which target a large number of final state signatures, and we derive the most up to date limits on the MUED parameter space from 13 TeV SUSY searches. Universal Extra Dimensions -Introduction and Review.-Models with universal extra dimensions (UED) [1] represent a simple extension of the Standard Model which include a dark matter candidate and are testable at the LHC.[2] The extra-dimensions are universal in the sense that all Standard Model (SM)fields are promoted to fields which propagate on the full space-time M × X, where M is the flat four dimensional (4D) Minkowski space and X is a compact space. As X is compact, the momenta along the extradimensions are discretized. In the 4D effective theory, each extra-dimensional field yields a 4D field without extra-dimensional momentum (the zero-mode which is to be identified with the 4D SM field) as well as a Kaluza-Klein (KK) tower of excitations which are heavy partner states with the same quantum numbers as the zero-mode. The KK mass spectrum is determined by the inverse size and the geometry of the extra-dimensions. In the simplest case of only one extra dimension, -which we focus on in this letter -compactification on the orbifold X = S 1 /Z 2 allows to have chiral zero-modes of fermions and A µ zero-mode for gauge fields without an additionalThe 5D UED model appears to be a very simple and predictive model as it seems to have only one parameter beyond the Standard Model (BSM), the compactification radius R. However, as a 5D theory, the model is inherently non-renormalizable and can only be considered as an effective theory, valid below a cutoff scale Λ, which introduces an additional parameter into the model. Naive dimensional analysis [4-7] and bounds from unitarity violation in gluon KK mode scattering [8] suggest that the cutoff is rather low: ΛR O(10 − 50). As a consequence, higher-dimensional operators at the cutoff scale can be phenomenologically relevant. [9] In the 5D minimal UED (MUED) model [10], all higher-dimensional operators are assumed to be absent at the cutoff scale Λ, and they are only induced at lower energies due to renormalization group running, thus keeping the model a simple BSM scenario with only two parameters: the inverse compactification radius R −1 which sets the mass scale of the first KK excitations, i.e. of the lightest partners of the SM fields, and ΛR, which controls the number of KK m...