On discrete symmetries and torsion homology in F-theory

Christoph Mayrhofer, Eran Palti, Oskar Till, Timo Weigand

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


Abstract: We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a ℤ2$$ {\mathbb{Z}}_2 $$ symmetry, we show that there are two physically distinct ways that such a discrete gauge symmetry can arise. First, compactifications of M-Theory on Calabi-Yau threefolds which support a genus-one fibration with a bi-section are known to be dual to six-dimensional F-theory vacua with a ℤ2$$ {\mathbb{Z}}_2 $$ gauge symmetry. We show that the resulting five-dimensional theories do not have a ℤ2$$ {\mathbb{Z}}_2 $$ symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit torsion in homology. Associated to the bi-section fibration is a Jacobian fibration which does support a section. Compactifying on these related but distinct varieties does lead to a ℤ2$$ {\mathbb{Z}}_2 $$ symmetry in five dimensions and, accordingly, we find explicitly an associated torsion cycle. We identify the expected particle and membrane system of the discrete symmetry in terms of wrapped M2 and M5 branes and present a field-theory description of the physics for both cases in terms of circle reductions of six-dimensional theories. Our results and methods generalise straightforwardly to larger discrete symmetries and to four-dimensional compactifications.

Original languageEnglish
Article number29
JournalJournal of High Energy Physics
Issue number6
StatePublished - 8 Jun 2015
Externally publishedYes


  • Discrete and Finite Symmetries
  • F-Theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


Dive into the research topics of 'On discrete symmetries and torsion homology in F-theory'. Together they form a unique fingerprint.

Cite this