2022/05/20 by Abhiram Kidambi, Kidambi, Abhiram, Masaki Okada +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Compactification (mathematics) #Conformal map #FOS: Mathematics #FOS: Physical sciences #Field (mathematics) #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Mathematical analysis #Mathematics #Moduli space #Number Theory (math.NT) #Physics #Pure mathematics #Rational number #Theoretical physics #hep-th #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.2205.10299
published in arXiv (Cornell University) (Cornell University) · In v.2, numerous small errors and typos are corrected, and a little more explanations, a few figures and references are added
openalex publication_date 2022/05/20 · arxiv created 2022/06/10 · arxiv updated 2022/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The study of rational conformal field theories in the moduli space is of particular interest since these theories correspond to points in moduli space where the algebraic and arithmetic structure are usually richer, while also being points where non--trivial physics occurs (such as in the study of attractor black holes and BPS states at rational points). This has led to various attempts to characterize and classify such rational points. In this paper, a conjectured characterization by Gukov--Vafa of rational conformal field theories whose target space is a Ricci flat Kähler manifold is analyzed carefully for the case of toroidal compactifications. We refine the conjectured statement as well as making an effort to verify it, using T4 compactification as a test case. Seven common properties in terms of Hodge theory (including complex multiplication) have been identified for T4-target rational conformal field theories. By imposing three properties out of the seven, however, there remain \mathcal N = (1,1) SCFTs that are not rational. Open questions, implications and future lines of work are discussed.