2024/08/01 by Abhiram Kidambi, Kidambi, Abhiram, Masaki Okada +3
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Combinatorics #Computer science #FOS: Physical sciences #Geometry #High Energy Physics - Theory (hep-th) #Mathematics #Mirror symmetry #Multiplication (music) #Physics #Pure mathematics #Symmetry (geometry) #Theoretical physics
paper · pdf · doi:10.48550/arxiv.2408.00861
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/08/01 · openalex created_date 2025/01/13 · openalex updated_date 2026/08/01
These notes combine results from two papers by the present authors viz., Part I (arXiv:2205.10299) and Part II (arXiv:2212.13028) into one streamlined version for better readability, along with a review on theory of complex multiplication for non-singular complex projective varieties and complex tori that is aimed at string theorists. We think that it is worth posting this edition as a separate entry in arXiv for those reasons, although this edition contains no essential progress beyond Part I and Part II. S. Gukov and C. Vafa proposed a characterization of rational N=(1,1) superconformal field theories (SCFTs) on 1+1 dimensions with Ricci-flat Kahler target spaces in terms of the Hodge structure of the target space, extending an earlier observation by G. Moore. We refined this idea and obtained a conjectural statement on necessary and sufficient conditions for such SCFTs to be rational, which we indeed prove to be true in the case the target space is T4. In the refined statement, the algebraicity of the geometric data of the target space turns out to be essential, and the Strominger--Yau--Zaslow fibration in the mirror correspondence also plays a vital role.