On discrete symmetries and torsion homology in F-theory

• DOI: 10.1007/jhep06(2015)029
• Publication Date: 2015-06-05T12:42:04Z
• Authors: Christoph Mayrhofer; Eran Palti; Oskar Till; Timo Weigand
• Keywords: Discrete symmetry; F-theory; Homology

We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on associated Calabi-Yau manifold. Focusing simplest example of a $$ {\mathbb{Z}}_2 symmetry, we show that there are two physically distinct ways such symmetry can arise. First, M-Theory threefolds which support genus-one fibration with bi-section known to be dual six-dimensional vacua symmetry. resulting five-dimensional theories do not have but latter emerges only decompactification limit. Accordingly fibred manifolds exhibit homology. Associated is Jacobian does section. Compactifying these related varieties lead five dimensions and, accordingly, find explicitly an cycle. identify expected particle membrane system terms wrapped M2 M5 branes present field-theory description physics for both cases circle reductions theories. Our results methods generalise straightforwardly larger four-dimensional compactifications.