The A-decomposability of the Singer construction

Let $R_s M$ denote the Singer construction on an unstable module $M$ over the Steenrod algebra $A$ at the prime two; $R_s M$ is canonically a subobject of $P_s\otimes M$, where $P_s$ is the polynomial algebra on s generators of degree one. Passage to $A$-indecomposables gives the natural transformation $R_s M \rightarrow F \otimes_A (P_s \otimes M)$, which identifies with the dual of the composition of the Singer transfer and the Lannes-Zarati homomorphism. The main result of the paper proves the weak generalized algebraic spherical class conjecture, which was proposed by the first named author. Namely, this morphism is trivial on elements of positive degree when s>2. The condition s>2 is necessary, as exhibited by the spherical classes of Hopf invariant one and those of Kervaire invariant one.Comment: v2 15 pages. Minor revision. v3 17 pages, revision following referee's recommendations. Accepted for publication J. Al

Question of Peccei-Quinn symmetry and quark masses in the economical 3-3-1 model

We show that there is an infinite number of U(1) symmetries like Peccei-Quinn symmetry in the 3-3-1 model with minimal scalar sector---two scalar triplets. Moreover, all of them are completely broken due to the model's scalars by themselves (notice that these scalars as known have been often used to break the gauge symmetry and generating the masses for the model's particles). There is no any residual Peccei-Quinn symmetry. Because of the minimal scalar content there are some quarks that are massless at tree-level, but they can get consistent mass contributions at one-loop due to this fact. Interestingly, axions as associated with the mentioned U(1)s breaking (including Majoron due to lepton-charge breaking) are all gauged away because they are also the Goldstone bosons responsible for the gauge symmetry breaking as usual.Comment: 25 pages, 4 figures, revised version, to appear in Physical Review

Quantum many-body models with cold atoms coupled to photonic crystals

Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, as atoms are nominally neutral point particles, this limits the types of interactions that can be produced. We propose to use the powerful new platform of cold atoms trapped near nanophotonic systems to extend these limits, enabling a novel quantum material in which atomic spin degrees of freedom, motion, and photons strongly couple over long distances. In this system, an atom trapped near a photonic crystal seeds a localized, tunable cavity mode around the atomic position. We find that this effective cavity facilitates interactions with other atoms within the cavity length, in a way that can be made robust against realistic imperfections. Finally, we show that such phenomena should be accessible using one-dimensional photonic crystal waveguides in which coupling to atoms has already been experimentally demonstrated

Large signal of h→μτh \rightarrow \mu \tau within the constraints of ei→ejγe_i \rightarrow e_j\gamma decays in the 3-3-1 model with neutral leptons

In the framework of the 3-3-1 model with neutral leptons, we have investigated the lepton-flavor-violating sources based on the Higgs mass spectrum which has two neutral Higgses identitied with corresponding ones in the Two-Higgs-Doublet model (THDM). On the $13~\mathrm{TeV}$ scale of the LHC, we point out the parameter space regions where the experimental limits of $e_i \rightarrow e_j\gamma$ decays are satisfied. These regions depend heavily on the mixing of exotic leptons but are predicted to have large $h^0_1\rightarrow \mu \tau$ signals. We also show that $\mathrm{Br}(h^0_1\rightarrow \mu \tau)$ can reach a value of $10^{-4}$.Comment: 30 pages, 9 figure

Poincar\'e gauge theory with even and odd parity dynamic connection modes: isotropic Bianchi cosmological models

The Poincar\'e gauge theory of gravity has a metric compatible connection with independent dynamics that is reflected in the torsion and curvature. The theory allows two good propagating spin-0 modes. Dynamical investigations using a simple expanding cosmological model found that the oscillation of the 0$^+$ mode could account for an accelerating expansion similar to that presently observed. The model has been extended to include a $0^{-}$ mode and more recently cross parity couplings. We investigate the dynamics of this model in a situation which is simple, non-trivial, and yet may give physically interesting results that might be observable. We consider homogeneous cosmologies, more specifically, isotropic Bianchi class A models. We find an effective Lagrangian for our dynamical system, a system of first order equations, and present some typical dynamical evolution.Comment: 8 pages, 1 figures, submitted to IARD 2010 Conference Proceedings in {\em Journal of Physics: Conference Series}, eds. L. Horwitz and M. Land (2011