Editing Mirror symmetry (string theory) (section)

{{short description|In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds}}
{{String theory}}
{{Other uses|Mirror symmetry (disambiguation){{!}}Mirror symmetry}}
In [[algebraic geometry]] and [[theoretical physics]], '''mirror symmetry''' is a relationship between [[geometry|geometric]] objects called [[Calabi–Yau manifold]]s. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as [[extra dimension]]s of [[string theory]].

Early cases of mirror symmetry were discovered by physicists. Mathematicians became interested in this relationship around 1990 when [[Philip Candelas]], [[Xenia de la Ossa]], Paul Green, and Linda Parkes showed that it could be used as a tool in [[enumerative geometry]], a branch of mathematics concerned with counting the number of solutions to geometric questions. Candelas and his collaborators showed that mirror symmetry could be used to count [[rational curve]]s on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of its mathematical predictions have since been [[mathematical proof|proven rigorously]].

Today, mirror symmetry is a major research topic in [[pure mathematics]], and mathematicians are working to develop a mathematical understanding of the relationship based on physicists' intuition. Mirror symmetry is also a fundamental tool for doing calculations in string theory, and it has been used to understand aspects of [[quantum field theory]], the formalism that physicists use to describe [[elementary particles]]. Major approaches to mirror symmetry include the [[homological mirror symmetry]] program of [[Maxim Kontsevich]], and the [[SYZ conjecture]] of [[Andrew Strominger]], [[Shing-Tung Yau]], and [[Eric Zaslow]] and its algebraic analog — the Gross-Siebert program of [[Mark Gross (mathematician)|Mark Gross]] and [[Bernd Siebert]].