Quartic gauge couplings from $K3$ geometry

Abstract

We show how certain F 4 couplings in eight dimensions can be computed using the mirror map and K3 data.They perfectly match with the corresponding heterotic one-loop couplings, and therefore this amounts to a successful test of the conjectured duality between the heterotic string on T 2 and F-theory on K3.The underlying quantum geometry appears to be a 5-fold, consisting of a hyperkahler 4-fold fibered over a P 1 base.The natural candidate for this fiber is the symmetric product Sym 2 (K3).We are lead to this structure by analyzing the implications of higher powers of E2 in the relevant Borcherds counting functions, and in particular the appropriate generalizations of the Picard-Fuchs equations for the K3.

Locations

• Advances in Theoretical and Mathematical Physics - View - PDF
• arXiv (Cornell University) - View - PDF
• CERN Document Server (European Organization for Nuclear Research) - View - PDF