W=0 Complex Structure Moduli Stabilization on CM-type K3 x K3 Orbifolds:---Arithmetic, Geometry and Particle Physics---
Abstract
It is an important question in string compactification whether complex structure moduli stabilization inevitably ends up with a vacuum expectation value of the superpotential < W > of the order of the Planck scale cubed. Any thoughts on volume stabilization and inflation in string theory, as well as on phenomenology of supersymmetric Standard Models, will be affected by the answer to this question. In this work, we follow an idea for making < W > 0 where the internal manifold has a vacuum complex structure with arithmetic characterization, and address Calabi--Yau fourfold compactification of F-theory. The moduli space of K3 x K3 orbifolds contain infinitely many such vacua. Arithmetic conditions for a < W > =0 flux are worked out, and then all the K3 moduli have supersymmetric mass. Possible gauge groups, matter representations and discrete symmetries are studied for the case of Z_2-orbifolds.
Cite
@article{arxiv.2012.01111,
title = {W=0 Complex Structure Moduli Stabilization on CM-type K3 x K3 Orbifolds:---Arithmetic, Geometry and Particle Physics---},
author = {Keita Kanno and Taizan Watari},
journal= {arXiv preprint arXiv:2012.01111},
year = {2021}
}
Comments
70 pages; in v2, reference added and typo corrected; in v3, fixed an error in section 2.2 (v2), and improved understanding on E7-56 matter multiplicity in section 4.3