Calabi-Yau threefolds

Calabi-Yau threefolds are complex, six-dimensional shapes used in string theory to model the universe’s hidden dimensions. They are geometric spaces with special properties: they are compact, complex, and Ricci-flat, meaning they have no intrinsic curvature. These shapes are crucial because they allow extra dimensions—beyond our familiar three—to remain consistent with physical laws, influencing how particles and forces behave. Imagine them as intricate, folded spaces that, while imperceptible to us, shape the fundamental properties of our universe at a deep mathematical level.