Gauge Coupling Unification in E6 F-Theory GUTs with Matter and Bulk Exotics from Flux Breaking

We consider gauge coupling unification in E6 F-Theory Grand Unified Theories (GUTs) where E6 is broken to the Standard Model (SM) gauge group using fluxes. In such models there are two types of exotics that can affect gauge coupling unification, namely matter exotics from the matter curves in the 27 dimensional representation of E6 and the bulk exotics from the adjoint 78 dimensional representation of E6. We explore the conditions required for either the complete or partial removal of bulk exotics from the low energy spectrum. In the latter case we shall show that (miraculously) gauge coupling unification may be possible even if there are bulk exotics at the TeV scale. Indeed in some cases it is necessary for bulk exotics to survive to the TeV scale in order to cancel the effects coming from other TeV scale matter exotics which would by themselves spoil gauge coupling unification. The combination of matter and bulk exotics in these cases can lead to precise gauge coupling unification which would not be possible with either type of exotics considered by themselves. The combination of matter and bulk exotics at the TeV scale represents a unique and striking signature of E6 F-theory GUTs that can be tested at the LHC.Comment: 21 pages, 5 figure

Involutions and the Gelfand character

The Gelfand representation of $\mathcal{S}_n$ is the multiplicity-free direct sum of the irreducible representations of $\mathcal{S}_n$. In this paper, we use a result of Adin, Postnikov, and Roichman to find a recursive generating function for the Gelfand character. In order to find this generating function, we investigate descents of so-called $\lambda$-unimodal involutions

Proof of Luck: an Efficient Blockchain Consensus Protocol

In the paper, we present designs for multiple blockchain consensus primitives and a novel blockchain system, all based on the use of trusted execution environments (TEEs), such as Intel SGX-enabled CPUs. First, we show how using TEEs for existing proof of work schemes can make mining equitably distributed by preventing the use of ASICs. Next, we extend the design with proof of time and proof of ownership consensus primitives to make mining energy- and time-efficient. Further improving on these designs, we present a blockchain using a proof of luck consensus protocol. Our proof of luck blockchain uses a TEE platform's random number generation to choose a consensus leader, which offers low-latency transaction validation, deterministic confirmation time, negligible energy consumption, and equitably distributed mining. Lastly, we discuss a potential protection against up to a constant number of compromised TEEs.Comment: SysTEX '16, December 12-16, 2016, Trento, Ital

Precision measurement of the 5 2S1/2 - 4 2D5/2 quadrupole transition isotope shift between 88Sr+ and 86Sr+

We have measured the isotope shift of the narrow quadrupole-allowed 5 2S1/2 - 4 2D5/2 transition in 86Sr+ relative to the most abundant isotope 88Sr+. This was accomplished using high-resolution laser spectroscopy of individual trapped ions, and the measured shift is Delta-nu_meas^(88,86) = 570.281(4) MHz. We have also tested a recently developed and successful method for ab-initio calculation of isotope shifts in alkali-like atomic systems against this measurement, and our initial result of Delta-nu_calc^(88,86) = 457(28) MHz is also presented. To our knowledge, this is the first high precision measurement and calculation of that isotope shift. While the measurement and the calculation are in broad agreement, there is a clear discrepancy between them, and we believe that the specific mass shift was underestimated in our calculation. Our measurement provides a stringent test for further refinements of theoretical isotope shift calculation methods for atomic systems with a single valence electron

Bimaximal Mixings from the Texture of the Right-handed Majorana Neutrino Mass Matrix

We study the origin of neutrino masses and mixing angles which can accomodate the LMA MSW solutions of the solar neutrino anomaly as well as the solution of the atmospheric neutrino problem, within the framework of the see-saw mechanism. We employ the diagonal form of the Dirac neutrino mass matrices with the physical masses as diagonal elements in the hierarchical order. Such choice has been motivated from the fact that the known CKM angles for the quark sector, are relatively small. We consider both possibilities where the Dirac neutrino mass matrix is either the charged lepton or the up-quark mass matrix within the framework of SO(10) GUT with or without supersymmetry. The non-zero texture of the right-handed Majorana neutrino mass matrix $M_{R}$ is used for the generation of the desired bimaximal mixings in a model independent way. Both hierarchical and inverted hierarchical models of the left-handed Majorana neutrino mass matrices are generated and then discussed with examples

Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models

Recent T2K results indicate a sizeable reactor angle theta_13 which would rule out exact tri-bimaximal lepton mixing. We study the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1' and 1" representations and show that it leads to trimaximal mixing in which the second column of the lepton mixing matrix consists of the column vector (1,1,1)^T/sqrt{3}, with a potentially large reactor angle. In order to limit the reactor angle and control the higher order corrections, we propose a renormalisable S4 model in which the 1' and 1" flavons of A4 are unified into a doublet of S4 which is spontaneously broken to A4 by a flavon which enters the neutrino sector at higher order. We study the vacuum alignment in the S4 model and show that it predicts accurate trimaximal mixing with approximate tri-bimaximal mixing, leading to a new mixing sum rule testable in future neutrino experiments. Both A4 and S4 models preserve form dominance and hence predict zero leptogenesis, up to renormalisation group corrections.Comment: 24 pages, 2 figures, version to be published in JHE