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 hyperk"ahler 4-fold fibered over a IP^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 E_2 in the relevant Borcherds counting functions, and in particular the appropriate generalizations of the Picard-Fuchs equations for the K3.

32 p, harvmac; One footnote on page 11 extended; results unchanged; Version subm. to ATMP

Cited by in corpus (6)

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• A note on heterotic/type I' duality and D0 brane quantum mechanics
• D1/D5 systems in $\mathcal{N}=4$ string theories
• Prepotentials from Symmetric Products