Kavli Affiliate: Taizan Watari
| First 5 Authors: Abhiram Kidambi, Masaki Okada, Taizan Watari, ,
| Summary:
The study of rational conformal field theories is of particular interest in
the moduli space of conformal field theories since such rational points
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 K"ahler 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 $T^4$ compactification as a test case. Seven common
properties in terms of Hodge theory (including complex multiplication) have
been identified for $T^4$-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.
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