Fixing All Moduli for M-Theory on K3xK3
Paul S. Aspinwall, Renata Kallosh
TL;DR
This work analyzes M-theory on K3xK3 with G-flux preserving half the supersymmetry and its F-theory orientifold limit to type IIB on K3x(T^2/Z_2). It proves a finite, classifiable set of attractive K3 pairs, yielding 13 flux configurations (8 orientifold-compatible) under the tadpole constraint, and shows that G-flux fixes the complex structures while leaving 40 real Kahler moduli to be fixed by M5-brane instantons. The central mechanism involves instanton corrections from M5 wrapping divisors of the form S1×P^1 or P^1×S2 with flux-modified zero modes that generate a nonperturbative superpotential, generically isolating and fixing all moduli; in the orientifold limit these correspond to D3-instantons in K3×(T^2/Z_2). Overall, the paper demonstrates a coherent pathway to full moduli stabilization in a simple yet rich M-theory/F-theory orientifold setting and clarifies how flux and instanton effects collaborate to fix geometric and axio-dilaton moduli.
Abstract
We analyze M-theory compactified on K3xK3 with fluxes preserving half the supersymmetry and its F-theory limit, which is dual to an orientifold of the type IIB string on $K3\times T^2/Z_2$. The geometry of attractive K3 surfaces plays a significant role in the analysis. We prove that the number of choices for the K3 surfaces is finite and we show how they can be completely classified. We list the possibilities in one case. We then study the instanton effects and see that they will generically fix all of the moduli. We also discuss situations where the instanton effects might not fix all the moduli.