Journal of Undergraduate Research
Keywords
duality, Calabi-Yau manifolds, Landau-Ginzburg, mirror symmetry
College
Physical and Mathematical Sciences
Department
Mathematics
Abstract
Suppose you have a physical system that can jump suddenly between two stable states. Then a function modeling the system will have a singularity at the jump. Our singularities will all be defined by polynomials, such as x3y + y5 + z2. Mathematician V.I. Arnol’d studied such singularities in an abstract setting, and he noticed that a certain 14 singularities came in pairs: numbers describing two di erent aspects of these singularities matched each singularity with its \dual” partner, which had the same numbers but with reversed roles (see Table 1). Arnol’d found no mathematical or physical reason why these singularities should be partnered in this way; hence, he dubbed the phenomenon a strange duality. This duality has fascinated mathematicians ever since, prompting explanations from multiple branches of mathematics.
Recommended Citation
Suggs, Rachel and Jarvis, Dr. Tyler
(2013)
"An Explanation of Strange Duality in terms of Landau-Ginzburg Mirror Symmetry,"
Journal of Undergraduate Research: Vol. 2013:
Iss.
1, Article 2703.
Available at:
https://scholarsarchive.byu.edu/jur/vol2013/iss1/2703