A holographic model for hall viscosity

We have modified the holographic model of Saremi and Son [12] by using a charged black brane, instead of a neutral one, such that when the bulk pseudo scalar (θ  ) potential is made of θ²${\theta }^2$ and θ⁴${\theta }^4$ terms, parity can still be broken spontaneously in the boundary theory. In our model, the 3+1$3+1$ dimensional bulk has a pseudo scalar coupled to the gravitational Chern–Simons term in the anti de Sitter charged black brane back ground. Parity could be broken spontaneously in the bulk by the pseudo scalar hairy solution and give rise to non-zero Hall viscosity at the boundary theory.     

Electroweak instantons,axions, and the cosmological constant

If there is explicit violation of baryon plus lepton number at some energy scale, then the electroweak theory depends upon a θ-angle. Due to a singular integration over small scale size instantons, this θ  -dependence is sensitive to very high momentum scales. Assuming that there is no new physics between the electroweak and Planck scales, for an electroweak axion the energy difference between the vacuum at θ≠0$\theta \ne 0$, and that at θ=0$\theta =0$, is of the correct order of magnitude to be the dark energy observed in the present epoch.     

Non-standard interaction effects at reactor neutrino experiments

We study non-standard interactions (NSIs) at reactor neutrino experiments, and in particular, the mimicking effects on θ₁₃${\theta }_{13}$. We present generic formulas for oscillation probabilities including NSIs from sources and detectors. Instructive mappings between the fundamental leptonic mixing parameters and the effective leptonic mixing parameters are established. In addition, NSI corrections to the mixing angles θ₁₃${\theta }_{13}$ and θ₁₂${\theta }_{12}$ are discussed in detailed. Finally, we show that, even for a vanishing θ₁₃${\theta }_{13}$, an oscillation phenomenon may still be observed in future short baseline reactor neutrino experiments, such as Double Chooz and Daya Bay, due to the existences of NSIs.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.     

Avoiding the big-rip jeopardy in a quintom dark energy model with higher derivatives

In the framework of a single scalar field quintom model with higher derivative, we construct in this Letter a dark energy model of which the equation of state (EOS) w   crosses over the cosmological constant boundary. Interestingly during the evolution of the universe w<−1$w<-1$ happens just for a period of time with a distinguished feature that w   starts with a value above −1, transits into w<−1$w<-1$, then comes back to w>−1$w>-1$. This avoids the big-rip jeopardy induced by w<−1$w<-1$.     

Half-monopole in the Weinberg–Salam model

We present new axially symmetric half-monopole configuration of the SU(2)×U(1) Weinberg–Salam model of electromagnetic and weak interactions. The half-monopole configuration possesses net magnetic charge 2π/e$2\pi /e$ which is half the magnetic charge of a Cho–Maison monopole. The electromagnetic gauge potential is singular along the negative z$z$-axis. However the total energy is finite and increases only logarithmically with increasing Higgs field self-coupling constant λ^1/2${\lambda }^{1/2}$ at sin²θ_W=0.2312${sin}^2{\theta }_W=0.2312$. In the U(1) magnetic field, the half-monopole is just a one dimensional finite length line magnetic charge extending from the origin r=0$r=0$ and lying along the negative z$z$-axis. In the SU(2) ’t Hooft magnetic field, it is a point magnetic charge located at r=0$r=0$. The half-monopole possesses magnetic dipole moment that decreases exponentially fast with increasing Higgs field self-coupling constant λ^1/2${\lambda }^{1/2}$ at sin²θ_W=0.2312${sin}^2{\theta }_W=0.2312$.     

Finite quantum corrections to the tribimaximal neutrino mixing

We calculate finite   quantum corrections to the tribimaximal neutrino mixing pattern VTB$V_{\mathrm{TB}}$ in three generic classes of neutrino mass models. We show that three flavor mixing angles can all depart from their tree-level results described by VTB$V_{\mathrm{TB}}$, among which θ₁₂${\theta }_{12}$ is most sensitive to such quantum effects, and the Dirac CP-violating phase can radiatively arise from two Majorana CP-violating phases. This theoretical scheme offers a new way to understand why θ₁₃${\theta }_{13}$ is naturally small and how three CP-violating phases are presumably correlated.     

Vortices and Jacobian varieties

We investigate the geometry of the moduli space of N$N$ vortices on line bundles over a closed Riemann surface Σ$\Sigma$ of genus g>1$g>1$, in the little explored situation where 1≤N<g$1\le N<g$. In the regime where the area of the surface is just large enough to accommodate N$N$ vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of Σ$\Sigma$. For N=1$N=1$, we show that the metric on the moduli space converges to a natural Bergman metric on Σ$\Sigma$. When N>1$N>1$, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel–Jacobi map of Σ$\Sigma$ at degree N$N$. We describe consequences of this phenomenon from the point of view of multivortex dynamics.     

Zero finite-temperature charge stiffness within the half-filled 1D Hubbard model

Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0$T>0$ transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0$T=0$ 1D insulator the charge stiffness D(T)$D\left(T\right)$ vanishes for T>0$T>0$ and finite values of the on-site repulsion U$U$ in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T$T$ and U>0$U>0$ it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0$U=0$ and vanishes for U>0$U>0$ is found to result from a general transition from a conductor to an insulator or resistor occurring at U=U_c=0$U=U_c=0$ for all finite temperatures T>0$T>0$. (At T=0$T=0$ such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the η$\eta$-spin SU(2)$SU\left(2\right)$ symmetry with the hidden U(1)$U\left(1\right)$ symmetry beyond SO(4)$SO\left(4\right)$ is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model.     

If Gauss–Bonnet interaction plays the role of dark energy

A cosmological model has been constructed with Gauss–Bonnet-scalar interaction, where the Universe starts with exponential expansion but encounters infinite deceleration, q→∞$q\to \infty$ and infinite equation of state parameter, w→∞$w\to \infty$. During evolution it subsequently passes through the stiff fluid era, q=2$q=2$, w=1$w=1$, the radiation dominated era, q=1$q=1$, w=1/3$w=1/3$ and the matter dominated era, q=1/2$q=1/2$, w=0$w=0$. Finally, deceleration halts, q=0$q=0$, w=−1/3$w=-1/3$, and it then encounters a transition to the accelerating phase. Asymptotically the Universe reaches yet another inflationary phase q→−1$q\to -1$, w→−1$w\to -1$. Such evolution is independent of the form of the potential and the sign of the kinetic energy term, i.e., even a non-canonical kinetic energy is unable to phantomize (w<−1)$(w<-1)$ the model.     

Entanglement entropy and variational methods: Interacting scalar fields

We develop a variational approximation to the entanglement entropy for scalar ?⁴${?}^4$ theory in 1+1$1+1$, 2+1$2+1$, and 3+1$3+1$ dimensions, and then examine the entanglement entropy as a function of the coupling. We find that in 1+1$1+1$ and 2+1$2+1$ dimensions, the entanglement entropy of ?⁴${?}^4$ theory as a function of coupling is monotonically decreasing and convex. While ?⁴${?}^4$ theory with positive bare coupling in 3+1$3+1$ dimensions is thought to lead to a trivial free theory, we analyze a version of ?⁴${?}^4$ with infinitesimal negative bare coupling, an asymptotically free theory known as precarious  ?⁴${?}^4$ theory, and explore the monotonicity and convexity of its entanglement entropy as a function of coupling. Within the variational approximation, the stability of precarious ?⁴${?}^4$ theory is related to the sign of the first and second derivatives of the entanglement entropy with respect to the coupling.     

Rigidity of noncompact complete Bach-flat manifolds

Let (M,g)$(M,g)$ be a noncompact complete Bach-flat manifold with positive Yamabe constant. We prove that (M,g)$(M,g)$ is flat if (M,g)$(M,g)$ has zero scalar curvature and sufficiently small _L2$L_2$ bound of curvature tensor. When (M,g)$(M,g)$ has nonconstant scalar curvature, we prove that (M,g)$(M,g)$ is conformal to the flat space if (M,g)$(M,g)$ has sufficiently small _L2$L_2$ bound of curvature tensor and _L4/3$L_{4/3}$ bound of scalar curvature.     

Cyclic groups and quantum logic gates

We present a formula for an infinite number of universal quantum logic gates, which are 4$4$ by 4$4$ unitary solutions to the Yang–Baxter (Y–B) equation. We obtain this family from a certain representation of the cyclic group of order n$n$. We then show that this discrete   family, parametrized by integers n$n$, is in fact, a small sub-class of a larger continuous   family, parametrized by real numbers θ$\theta$, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian.     

The mass hierarchy with atmospheric neutrinos at INO

We study the neutrino mass hierarchy at the magnetized Iron CALorimeter (ICAL) detector at India-based Neutrino Observatory with atmospheric neutrino events generated by the Monte Carlo event generator Nuance. We judicially choose the observables so that the possible systematic uncertainties can be reduced. The resolution as a function of both energy and zenith angle simultaneously is obtained for neutrinos and anti-neutrinos separately from thousand years un-oscillated atmospheric neutrino events at ICAL to migrate number of events from neutrino energy and zenith angle bins to muon energy and zenith angle bins. The resonance ranges in terms of directly measurable quantities like muon energy and zenith angle are found using this resolution function at different input values of θ₁₃${\theta }_{13}$. Then, the marginalized χ²s${\chi }^2\mathrm{s}$ are studied for different input values of θ₁₃${\theta }_{13}$ with its resonance ranges taking input data in muon energy and zenith angle bins. Finally, we find that the mass hierarchy can be explored up to a lower value of θ₁₃≈5°${\theta }_{13}\approx 5°$ with confidence level >95% in this set up.