Here is a quote from a link found at the Fermilab website,
Quote:
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Extra dimensions promise to solve many of current particle theory's nagging problems. They can explain the abundance of matter over antimatter, the surprisingly large number of elementary particles, and even dark matter—all phenomena that the Standard Model of particle physics fails to predict. This makes the concept of extra dimensions enticing. Yet in the empirical discipline of physics, extra dimensions face an embarrassing dilemma: so far, not a single shred of experimental evidence has been found to support their existence.
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It's all just mathematics so far. However, the search goes on,