Brief History of Classical Mirror Symmetry

Abstract

In the background to the discovery of the mirror symmetry hypothesis there exists an idea of compactifying extra 6 dimensions of 10-dimensional heterotic string theory in order to obtain a 4-dimensional grand unified theory that describes our real world. The complex 3-dimensional Calabi–Yau manifold is nothing but the compact 6-dimensional space used for this purpose. In this chapter, we explain why this idea came from particle physicists and give a brief exposition of the process of discovery of mirror symmetry. Lastly, we introduce the first striking result of classical mirror symmetry revealed by the celebrated paper by Candelas et al. (For details of compactification of string theory, we recommend readers to consult [1].)