Fixing All Moduli for M-Theory on K3xK3

TL;DR

This paper investigates M-theory on K3xK3 with fluxes, demonstrating that all moduli can be fixed through instanton effects and providing a classification of the geometric choices involved.

Contribution

It proves the finiteness and classification of K3 surface choices in M-theory compactifications and analyzes how instanton effects can fix all moduli.

Findings

Number of K3 choices is finite and classifiable

Instanton effects can generically fix all moduli

Situations exist where not all moduli are fixed

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.