Mirror Symmetry from Reflexive Polytopes

Abstract

There are two main theories used by physicists to explain the inner workings of the universe. General relativity is used to describe the very large, while quantum mechanics describes the very small. For decades, physicists have sought after a so-called unified field theory to combine these two models. Currently, the most widely accepted candidate for a unified field theory is known as string theory. In order to reconcile general relativity with quantum mechanics, string theory extends our classical 4D model of space-time into extra dimensions. At every unique point in our known four dimensions, these extra dimensions have the structure of Calabi-Yau varieties, or 6D algebraic varieties. There are always two Calabi-Yau varieties that produce a particular physical model. In mathematics, we call this phenomenon mirror symmetry.