Exotic matter on singular divisors in F-theory

We analyze exotic matter representations that arise on singular seven-brane configurations in F-theory. We develop a general framework for analyzing such representations, and work out explicit descriptions for models with matter in the 2-index and 3-index symmetric representations of SU($N$) and SU(2) respectively, associated with double and triple point singularities in the seven-brane locus. These matter representations are associated with Weierstrass models whose discriminants vanish to high order thanks to nontrivial cancellations possible only in the presence of a non-UFD algebraic structure. This structure can be described using the normalization of the ring of intrinsic local functions on a singular divisor. We consider the connection between geometric constraints on singular curves and corresponding constraints on the low-energy spectrum of 6D theories, identifying some new examples of apparent "swampland" theories that cannot be realized in F-theory but have no apparent low-energy inconsistency.Comment: 71 page

How does a developmental relationship mentoring model affect toxicity experienced in mentoring relationships?

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Detection of Exotic Massive Hadrons in Ultra High Energy Cosmic Ray Telescopes

We investigate the detection of exotic massive strongly interacting hadrons (uhecrons) in ultra high energy cosmic ray telescopes. The conclusion is that experiments such as the Pierre Auger Observatory have the potential to detect these particles. It is shown that uhecron showers have clear distinctive features when compared to proton and nuclear showers. The simulation of uhecron air showers, and its detection and reconstruction by fluorescence telescopes is described. We determine basic cuts in observables that will separate uhecrons from the cosmic ray bulk, assuming this is composed by protons. If these are composed by heavier nucleus the separation will be much improved. We also discuss photon induced showers. The complementarity between uhecron detection in accelerator experiments is discussed.Comment: 9 page 9 figure