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I will explain and prove the statement of the title. The proof relies on a recent result of Slofstra in combinatorial group theory and the hypergraph approach to contextuality.

Based on http://arxiv.org/abs/1607.05870.

Incommensurate charge order is a phenomenon in which the electrons in a crystal attempt to order with a period irrationally-related to that of

the lattice spacing. In the first half of this talk I will present recent work [1] in which we demonstrate that incommensurately charge-ordered systems can lower their free energy by forming quasicrystals: slices through higher-dimensional crystals with properties lying between  periodicity and disorder. The result potentially greatly increases the number of known, naturally-occuring quasicrystals from the two present examples, both of which were found in the same Siberian meteorite. In the second half I will present work from an ongoing experimental collaboration in which atomically-resolved scanning tunneling microscopy and atomic force microscopy on semiconducting monolayers of molybdenum diselenide (MoSe2) see conducting edge states along one-dimensional mirror twin boundaries. Remarkably, these edge states then develop their own energy gap via charge ordering [2]. We see a number of features suggestive of incommensurate order. By employing a simple analytical model we demonstrate that the effect is in fact a result of fine-tuning between charge ordering and quantum well physics coming from the small system size (on the order of thirty atoms).

[1] F. Flicker and Jasper van Wezel, Physical Review Letters 115, 236401

(2015), Natural 1D Quasicrystals from Incommensurate Charge Order

[2] S. Barja et al., Nature Physics 12, 751-757 (2016), Charge density

wave order in 1D mirror twin boundaries of single-layer MoSe2

We consider conformal blocks of two heavy operators and an arbitrary  number of light operators in a 1+1 dimensional CFT with large central charge. Using the monodromy method, these higher-point  conformal blocks are shown to factorize into products of 4-point conformal blocks in the heavy-light limit for a class of OPE channels. This result is reproduced by considering suitable worldline configurations in the bulk conical defect geometry. We apply the CFT results to calculate the entanglement entropy of an arbitrary number of  disjoint intervals for heavy states. The corresponding holographic entanglement entropy calculated via the minimal area prescription precisely matches these results from CFT.

We describe a new solution to the strong CP problem inspired by the massless up quark solution. At high energies, QCD is embedded in a SU(3)xSU(3)xSU(3) model, with each matter generation charged under a different site. Instanton effects are unsuppressed at the scale of Higgsing to the SM diagonal QCD, and a set of anomalous U(1)_PQ symmetries removes the low-energy strong CP phase. A non-zero theta parameter is generated at loop level near current bounds. Similar models can also lead to a heavy axion solution to the strong CP problem.

If heavy fields are present during inflation, they can leave an imprint in late-time cosmological observables. The main signature of these fields is a small amount of distinctly shaped non-Gaussianity, which if detected, would provide a wealth of information about the particle spectrum of the inflationary Universe. Here we investigate to what extent these signatures can be detected or constrained using futuristic 21-cm surveys. This part of my talk is based on 1610.06559. In the second part of my talk I will discuss how non-adiabatic production of heavy particles, as recently studied in 1606.00513, can generate an interesting and so far unconstrained class of non-Gaussianity in the CMB.