Terminal singularities, Milnor numbers, and matter in Ftheory
Abstract
We initiate a systematic investigation of Ftheory on elliptic fibrations with singularities which cannot be resolved without breaking the CalabiYau condition, corresponding to Qfactorial terminal singularities. It is the purpose of this paper to elucidate the physical origin of such noncrepant singularities in codimension two and to systematically analyze Ftheory compactifications containing such singularities. The singularities reflect the presence of localized matter states from wrapped M2branes which are not charged under any massless gauge potential. We identify a class of Qfactorial terminal singularities on elliptically fibered CalabiYau threefolds for which we can compute the number of uncharged localized hypermultiplets in terms of their associated Milnor numbers. These count the local complex deformations of the singularities. The resulting sixdimensional spectra are shown to be anomalyfree. We exemplify this in a variety of cases, including models with nonperturbative gauge groups with both charged and uncharged localized matter. The underlying mathematics will be discussed further in a forthcoming publication.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 January 2018
 DOI:
 10.1016/j.geomphys.2017.09.001
 arXiv:
 arXiv:1612.05646
 Bibcode:
 2018JGP...123...71A
 Keywords:

 Singular spaces;
 CalabiYau threefolds;
 String theory;
 Ftheory;
 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology
 EPrint:
 47 pages, 6 figures, 12 tables