Algebra-geometry equivalence in string theory

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SUMMARY

The discussion centers on the equivalence between geometric structures, specifically manifolds, and algebraic structures, particularly associative algebras, within the context of string theory. The concept of "mirror symmetry" is highlighted as a key aspect of this equivalence, although it is noted that it primarily pertains to relationships between manifolds in string theory. Additionally, a connection to category theory is mentioned, indicating a composition defined on one of the structures. The user seeks literature that explores these mathematical concepts inspired by string theory.

PREREQUISITES
  • Understanding of string theory fundamentals
  • Familiarity with geometric structures, particularly manifolds
  • Knowledge of algebraic structures, specifically associative algebras
  • Basic concepts of category theory
NEXT STEPS
  • Research "mirror symmetry in string theory" for detailed insights
  • Explore "geometric Langlands program" for connections to algebraic structures
  • Study "category theory applications in physics" to understand compositional structures
  • Investigate "associative algebras in string theory" for algebraic perspectives
USEFUL FOR

Mathematicians, theoretical physicists, and researchers interested in the intersection of geometry and algebra within string theory.

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I am looking for literature on a certain topic in mathematics inspired by string theory of which I have heard bits and pieces. Since I am not at all familiar with string theory and haven't found anything online, I was hoping someone more knowledgeable might recognize some of the keywords I remember.

The most important point was that there was a certain equivalence between geometric structures and algebraic ones. The geometric structures were manifolds and the algebraic structures were related to associative algebras, if I'm not mistaken. The manifolds could be used to represent some state of a string. The term "mirror symmetry" was also mentioned. From what I gathered mirror symmetry was this equivalence between geometric and algebraic structures, but from Wikipedia I understand that in the context of string theory "mirror symmetry" refers to a relation between manifolds only. For what its worth: there was also a connection to category theory by defining some kind of composition on one of the structures.

I apologize for the vagueness. Hopefully, my description will ring a bell for someone.
 
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