On Discrete Symmetries and Torsion Homology in F-Theory

Mayrhofer, Christoph and Palti, Eran and Till, Oskar and Weigand, Timo

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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 _s13_s178484_s192 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 _s13_s178484_s192 gauge symmetry. We show that the resulting five-dimensional theories do not have a _s13_s178484_s192 symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit discrete torsion. 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 _s13_s178484_s192 symmetry in five dimensions and, accordingly, we find explicitly an associated discrete torsion. 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.

Information

Published
2015 as article
JHEP, 06 - page(s): 029
Contact
Dr. Christoph Mayrhofer
Type
theoretical work
Links
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