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TOPIC: Lie group E8


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Title: Spontaneous B-L Breaking as the Origin of the Hot Early Universe
Authors: Wilfried Buchmüller, Valerie Domcke, Kai Schmitz

The decay of a false vacuum of unbroken B-L symmetry is an intriguing and testable mechanism to generate the initial conditions of the hot early universe. If B-L is broken at the grand unification scale, the false vacuum phase yields hybrid inflation, ending in tachyonic preheating. The dynamics of the B-L breaking Higgs field and thermal processes produce an abundance of heavy neutrinos whose decays generate entropy, baryon asymmetry and gravitino dark matter. We study the phase transition for the full supersymmetric Abelian Higgs model. For the subsequent reheating process we give a detailed time-resolved description of all particle abundances. The competition of cosmic expansion and entropy production leads to an intermediate period of constant 'reheating' temperature, during which baryon asymmetry and dark matter are produced. Consistency of hybrid inflation, leptogenesis and gravitino dark matter implies relations between neutrino parameters and superparticle masses, in particular a lower bound on the gravitino mass of 10 GeV.

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Title: The Point of E_8 in F-theory GUTs
Authors: Jonathan J. Heckman, Alireza Tavanfar, Cumrun Vafa
(Version v2)

We show that in F-theory GUTs, a natural explanation of flavor hierarchies in the quark and lepton sector requires a single point of E_8 enhancement in the internal geometry, from which all Yukawa couplings originate. The monodromy group acting on the seven-brane configuration plays a key role in this analysis. Moreover, the E_8 structure automatically leads to the existence of the additional fields and interactions needed for minimal gauge mediated supersymmetry breaking,__and almost nothing else__. Surprisingly, we find that in all but one Dirac neutrino scenario the messenger fields in the gauge mediated supersymmetry breaking sector transform as vector-like pairs in the 10 + 10* of SU(5). We also classify dark matter candidates available from this enhancement point, and rule out both annihilating and decaying dark matter scenarios as explanations for the recent experiments PAMELA, ATIC and FERMI. In F-theory GUT models, a 10-100 MeV mass gravitino remains as the prime candidate for dark matter, thus suggesting an astrophysical origin for recent experimental signals.

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The "exceptionally simple theory of everything," proposed by a surfing physicist in 2007, does not hold water, says Emory mathematician Skip Garibaldi.
Garibaldi, a rock climber in his spare time, did the math to disprove the theory, which involves a mysterious structure known as E8. The resulting paper, co-authored by physicist Jacques Distler of the University of Texas, will appear in an upcoming issue of Communications in Mathematical Physics.

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Title: There is no "Theory of Everything" inside E8
Authors: Jacques Distler, Skip Garibaldi
(Version v3)

We analyse certain subgroups of real and complex forms of the Lie group E8, and deduce that any "Theory of Everything" obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E8 lacks certain representation-theoretic properties required by physical reality. The arguments themselves amount to representation theory of Lie algebras in the spirit of Dynkin's classic papers and are written for mathematicians.

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Exotic symmetry seen in electrons

An exotic type of symmetry - suggested by string theory and theories of high-energy particle physics, and also conjectured for electrons in solids under certain conditions - has been observed experimentally for the first time.
An international team, led by scientists from Oxford University, report in a recent article in Science how they spotted the symmetry, termed E8, in the patterns formed by the magnetic spins in crystals of the material cobalt niobate, cooled to near absolute zero and subject to a powerful applied magnetic field.
The material contains cobalt atoms arranged in long chains and each atom acts like a tiny bar magnet that can point either 'up' or 'down'.
When a magnetic field is applied at right angles to the aligned spin directions, the spins can 'quantum tunnel' between the 'up' and 'down' orientations. At a precise value of the applied field these fluctuations 'melt' the ferromagnetic order of the material resulting in a 'quantum critical' state.

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Golden ratio discovered in a quantum world

Researchers from the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), in cooperation with colleagues from Oxford and Bristol Universities, as well as the Rutherford Appleton Laboratory, UK, have for the first time observed a nanoscale symmetry hidden in solid state matter. They have measured the signatures of a symmetry showing the same attributes as the golden ratio famous from art and architecture. The research team is publishing these findings in Science on the 8. January.
On the atomic scale particles do not behave as we know it in the macro-atomic world. New properties emerge which are the result of an effect known as the Heisenberg's Uncertainty Principle. In order to study these nanoscale quantum effects the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide and are a useful model for describing ferromagnetism on the nanoscale in solid state matter.
When applying a magnetic field at right angles to an aligned spin the magnetic chain will transform into a new state called quantum critical, which can be thought of as a quantum version of a fractal pattern.

"The system reaches a quantum uncertain - or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical"  - Prof. Alan Tennant, the leader of the Berlin group.

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F-theory GUTs
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Title: The Point of E_8 in F-theory GUTs
Authors: Jonathan J. Heckman, Alireza Tavanfar, Cumrun Vafa

We show that in F-theory GUTs, a natural explanation of flavour hierarchies in the quark and lepton sector requires a single point of E_8 enhancement in the internal geometry, from which all Yukawa couplings originate. The monodromy group acting on the seven-brane configuration plays a key role in this analysis. Moreover, the E_8 structure automatically leads to the existence of the additional fields and interactions needed for minimal gauge mediated supersymmetry breaking, and almost nothing else. Surprisingly, we find that in all but one Dirac neutrino scenario the messenger fields in the gauge mediated supersymmetry breaking sector transform as vector-like pairs in the 10 + 10* of SU(5). We also classify dark matter candidates available from this enhancement point, and rule out both annihilating and decaying dark matter scenarios as explanations for the recent experiments PAMELA, ATIC and FERMI. In F-theory GUT models, a 10-100 MeV mass gravitino remains as the prime candidate for dark matter, thus suggesting an astrophysical origin for recent experimental signals.

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E8_age10
Credit Garrett Lisi

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E8_ge9
Credit Garrett Lisi

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