When a quantum system is divided into subsystems, their entanglement entropies are subject to an inequality known as strong subadditivity. For a field theory this inequality can be stated as follows: given any two regions of space $A$ and $B$, $S(A)+S(B)\ge S(A\cup B)+S(A\cap B)$. Recently, a method has been found for computing entanglement entropies in any field theory for which there is a holographically dual gravity theory. We give a simple geometrical proof of strong subadditivity employing this holographic prescription.

This work presents a perturbative analysis of the supersymmetric Chern-Simons model in three spacetime dimensions coupled to a Higgs field, using the superfield formalism. We study the spontaneous symmetry breaking of the $U(1)$ gauge symmetry and evaluate the first quantum corrections to the effective action in the broken phase. We show that the infinite renormalization of the gap equation is enough to ensure the renormalizability of the model at the first loop level.

We obtain new charged rotating multi–black hole solutions on the Eguchi-Hanson space in the five-dimensional Einstein-Maxwell system with a Chern-Simons term and a positive cosmological constant. In the two-black holes case, these solutions describe the coalescence of two rotating black holes with the horizon topologies of ${\mathrm{S}}^3$ into a single rotating black hole with the horizon topology of the lens space $L(2;1)={\mathrm{S}}^3/{\mathbb{Z}}_2$. We discuss the differences in the horizon areas between our solutions and the two-centered Klemm-Sabra solutions which describe the coalescence of two rotating black holes with the horizon topologies of ${\mathrm{S}}^3$ into a single rotating black hole with the horizon topology of ${\mathrm{S}}^3$.

Bigravity is a natural arena where a nonlinear theory of massive gravity can be formulated. If the interaction between the metrics $f$ and $g$ is nonderivative, spherically symmetric exact solutions can be found. At large distances from the origin, these are generically Lorentz-breaking bi-flat solutions (provided that the corresponding vacuum energies are adjusted appropriately). The spectrum of linearized perturbations around such backgrounds contains a massless as well as a massive graviton, with two physical polarizations each. There are no propagating vectors or scalars, and the theory is ghost free (as happens with certain massive gravities with explicit breaking of Lorentz invariance). At the linearized level, corrections to general relativity are proportional to the square of the graviton mass, and so there is no van Dam-Veltam-Zakharov discontinuity. Surprisingly, the solution of linear theory for a static spherically symmetric source does not agree with the linearization of any of the known exact solutions. The latter coincide with the standard Schwarzschild-(anti)-de Sitter solutions of general relativity, with no corrections at all. Another interesting class of solutions is obtained where $f$ and $g$ are proportional to each other. The case of bi–de Sitter solutions is analyzed in some detail.

We propose that the late-time tail problem in the Reissner-Nordström (RN) spacetime is dual to a tail problem in the Schwarzschild spacetime with a different initial data set: at a fixed observation point the asymptotic decay rate of the fields are equal. This duality is used to find the decay rate for tails in RN. This decay rate is exactly as in Schwarzschild, including the case of the extremely-charged RN spacetime (ERN). The only case where any deviation from the Schwarzschild decay rate is found is the case of the tails along the event horizon of an ERN spacetime, where the decay rate is the same as at future null infinity. As observed at a fixed location, the decay rate in ERN is the same as in Schwarzschild. We verify these expectations with numerical simulations.

Statistical isotropy of primordial perturbations is a common assumption in cosmology, but it is an assumption that should be tested. To this end, we develop cosmic microwave background statistics for a primordial power spectrum that depends on the direction, as well as the magnitude, of the Fourier wave vector. We first consider a simple estimator that searches in a model-independent way for anisotropy in the square of the temperature (and/or polarization) fluctuation. We then construct the minimum-variance estimators for the coefficients of a spherical-harmonic expansion of the directional dependence of the primordial power spectrum. To illustrate, we apply these statistics to an inflation model with a quadrupole dependence of the primordial power spectrum on direction and find that a power quadrupole as small as 2.0% can be detected with the Planck satellite.

We present the performances and the strain sensitivity of the first spherical gravitational wave detector equipped with a capacitive transducer and readout by a low noise two-stage SQUID amplifier and operated at a temperature of 5 K. We characterized the detector performance in terms of thermal and electrical noise in the system output signal. We measured a peak strain sensitivity of $1.5\times {10}^{-20}{\mathrm{Hz}}^{-1/2}$ at 2942.9 Hz. A strain sensitivity of better than $5\times {10}^{-20}{\mathrm{Hz}}^{-1/2}$ has been obtained over a bandwidth of 30 Hz. We expect an improvement of more than 1 order of magnitude when the detector will operate at 50 mK. Our results represent the first step towards the development of an ultracryogenic omnidirectional detector sensitive to gravitational radiation in the 3 kHz range.

Symmetry-based ideas, such as the quark-lepton complementarity principle and the tribimaximal mixing scheme, have been proposed to explain the observed mixing pattern of neutrinos. We argue that such symmetry relations need to be imposed at a high scale $\Lambda \sim {10}^{12}\mathrm{GeV}$ characterizing the large masses of right-handed neutrinos required to implement the seesaw mechanism. For nonhierarchical neutrinos, renormalization group evolution down to a laboratory energy scale $\lambda \sim {10}^3\mathrm{GeV}$ tends to radiatively break these symmetries at a significant level and spoil the mixing pattern predicted by them. However, for Majorana neutrinos, suitable constraints on the extra phases ${\alpha }_{2,3}$ enable the retention of those high scale mixing patterns at laboratory energies. We examine this issue within the minimal supersymmetric standard model and demonstrate the fact posited above for two versions of quark-lepton complementarity and two versions of tribimaximal mixing. The appropriate constraints are worked out for all these four cases. Specifically, a preference for ${\alpha }_2\approx \pi$ (i.e., $m_1\approx -m_2$) emerges in each case. We also show how a future accurate measurement of ${\theta }_{13}$ may enable some discrimination among these four cases in spite of renormalization group evolution.

We compute the Coleman-Weinberg effective potential for the Higgs field in Randall-Sundrum Gauge-Higgs unification scenarios based on a bulk $SO(5)\times U(1{)}_X$ gauge symmetry, with gauge and fermion fields propagating in the bulk and a custodial symmetry protecting the generation of large corrections to the $T$ parameter and the coupling of the $Z$ to the bottom quark. We demonstrate that electroweak symmetry breaking may be realized, with proper generation of the top- and bottom-quark masses for the same region of bulk mass parameters that lead to good agreement with precision electroweak data in the presence of a light Higgs. We compute the Higgs mass and demonstrate that, for the range of parameters for which the Higgs boson has standard model-like properties, the Higgs mass is naturally in a range that varies between values close to the CERN LEP experimental limit and about 160 GeV. This mass range may be probed at the Tevatron and at the CERN LHC. We analyze the Kaluza-Klein spectrum and briefly discuss the phenomenology of the light resonances arising in our model.

The Hermitian Wilson kernel used in the construction of the domain-wall and overlap Dirac operators has exceptionally small eigenvalues that make it expensive to reach high-quality chiral symmetry for domain-wall fermions, or high precision in the case of the overlap operator. An efficient way of suppressing such eigenmodes consists of including a positive power of the determinant of the Wilson kernel in the Boltzmann weight, but doing this also suppresses tunneling between topological sectors. Here we propose a modification of the hybrid Monte-Carlo algorithm which aims to restore tunneling between topological sectors by excluding the lowest eigenmodes of the Wilson kernel from the molecular-dynamics evolution, and correcting for this at the accept/reject step. We discuss the implications of this modification for the acceptance rate.

We study the decay ${\Omega }^{-}\to {\Xi }^{-}{\pi }^{+}{\pi }^{-}$ in heavy-baryon chiral perturbation theory. At leading order, the decay is completely dominated by the ${\Xi }^{*0}(1530)$ intermediate state, and the predicted rate and ${\Xi }^{-}{\pi }^{+}$-mass distribution are in conflict with currently available data. It is possible to resolve this conflict by considering additional contributions at next-to-leading order.

The sensitivity of standard model Higgs boson searches at the Tevatron experiments with a mass $135<M_H<190\mathrm{GeV}/c^2$ using the channel $H\to W^{+}{W}^{-}\to l^{+}{l}^{-}{\mathrm{p̸}}_T(l=e,\mu )$ is discussed. Three new event selections involving Higgs in association with one or two high $P_T$ hadronic jets are discussed. Using leading order matrix elements and a conservative cut-based analysis a 95% confidence level exclusion on $\sigma \times \mathcal{B}(H\to W^{+}{W}^{-})$, 1.6 times larger than that predicted by the standard model for $M_H=165\mathrm{GeV}/c^2$, may be achieved with $5{\mathrm{fb}}^{-1}$ of integrated luminosity. By combining these three event selections with the existing analysis, the sensitivity of CDF and D0 could improve significantly.

I report the analysis performed on fermion masses and mixing, including neutrino mixing, within the context of a model with hierarchical radiative mass generation mechanism for light charged fermions, mediated by exotic scalar particles at one and two loops, respectively, meanwhile the neutrinos get Majorana mass terms at tree level through the Yukawa couplings with two $SU(2{)}_L$ Higgs triplets. All the resulting mass matrices in the model, for the $u$, $d$, and $e$ fermion charged sectors, the neutrinos and the exotic scalar particles, are diagonalized in exact analytical form. Quantitative analysis shows that this model is successful to accommodate the hierarchical spectrum of masses and mixing in the quark sector as well as the charged lepton masses. The lepton mixing matrix, $V_{\mathrm{PMNS}}$, is written completely in terms of the neutrino masses $m_1$, $m_2$, and $m_3$. Large lepton mixing for ${\theta }_{12}$ and ${\theta }_{23}$ is predicted in the range of values $0.7\lesssim {sin}^{2}2{\theta }_{12}\lesssim 0.7772$ and $0.87\lesssim {sin}^{2}2{\theta }_{23}\lesssim 0.9023$ by using $0.033\lesssim s_{13}^2\lesssim 0.04$. These values for lepton mixing are consistent with $3\sigma$ allowed ranges provided by recent global analysis of neutrino data oscillation. From $\Delta m_{\mathrm{sol}}^2$ bounds, neutrino masses are predicted in the range of values $m_1\approx (1.706–2.494)\times {10}^{-3}\mathrm{eV}$, $m_2\approx (6.675–12.56)\times {10}^{-3}\mathrm{eV}$, and $m_3\approx (1.215–2.188)\times {10}^{-2}\mathrm{eV}$, respectively. The above allowed lepton mixing leads to the quark-lepton complementary relations ${\theta }_{12}^{\mathrm{CKM}}+{\theta }_{12}^{\mathrm{PMNS}}\approx 41.543°–44.066°$ and ${\theta }_{23}^{\mathrm{CKM}}+{\theta }_{23}^{\mathrm{PMNS}}\approx 36.835°–38.295°$. The new exotic scalar particles induce flavor changing neutral currents and contribute to lepton flavor violating processes such as $E\to e_1{e}_2{e}_3$, to radiative rare decays, $\tau \to \mu \gamma$, $\tau \to e\gamma$, $\mu \to e\gamma$, as well as to the anomalous magnetic moments of fermions. I give general analytical expressions for the branching ratios of these rare decays and for the anomalous magnetic moments for charged leptons.

We present updated measurements of the branching fractions and $CP$ asymmetries for $B^0\to {\pi }^0{\pi }^0$, $B^{\pm }\to {\pi }^{\pm }{\pi }^0$, and $B^{\pm }\to K^{\pm }{\pi }^0$. Based on a sample of $383\times {10}^6$ $\mathit{{\rm Y}}(4S)\to B\overline{B}$ decays collected by the BABAR detector at the PEP-II asymmetric-energy $B$ factory at SLAC, we measure $\mathcal{B}(B^0\to {\pi }^0{\pi }^0)=(1.47\pm 0.25\pm 0.12)\times {10}^{-6}$, $\mathcal{B}(B^{\pm }\to {\pi }^{\pm }{\pi }^0)=(5.02\pm 0.46\pm 0.29)\times {10}^{-6}$, and $\mathcal{B}(B^{\pm }\to K^{\pm }{\pi }^0)=(13.6\pm 0.6\pm 0.7)\times {10}^{-6}$. We also measure the $CP$ asymmetries ${\mathcal{C}}_{{\pi }^0{\pi }^0}=-0.49\pm 0.35\pm 0.05$, ${\mathcal{A}}_{{\pi }^{\pm }{\pi }^0}=0.03\pm 0.08\pm 0.01$, and ${\mathcal{A}}_{K^{\pm }{\pi }^0}=0.030\pm 0.039\pm 0.010$. Finally, we present bounds on the Cabibbo-Kobayashi-Maskawa angle $\alpha$ using isospin relations.

We study the processes $e^{+}{e}^{-}\to 2({\pi }^{+}{\pi }^{-}){\pi }^0\gamma$, $2({\pi }^{+}{\pi }^{-})\eta \gamma$, $K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ and $K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}\eta \gamma$ with the hard photon radiated from the initial state. About 20 000, 4300, 5500, and 375 fully reconstructed events, respectively, are selected from $232{\mathrm{fb}}^{-1}$ of BABAR data. The invariant mass of the hadronic final state defines the effective $e^{+}{e}^{-}$ center-of-mass energy, so that the obtained cross sections from the threshold to about 5 GeV can be compared with corresponding direct $e^{+}{e}^{-}$ measurements, currently available only for the $\eta {\pi }^{+}{\pi }^{-}$ and $\omega {\pi }^{+}{\pi }^{-}$ submodes of the $e^{+}{e}^{-}\to 2({\pi }^{+}{\pi }^{-}){\pi }^0$ channel. Studying the structure of these events, we find contributions from a number of intermediate states, and we extract their cross sections where possible. In particular, we isolate the contribution from $e^{+}{e}^{-}\to \omega (782){\pi }^{+}{\pi }^{-}$ and study the $\omega (1420)$ and $\omega (1650)$ resonances. In the charmonium region, we observe the $J/\psi$ in all these final states and several intermediate states, as well as the $\psi (2S)$ in some modes, and we measure the corresponding branching fractions.

We calculate the electrical and thermal conductivities and the thermoelectric coefficient of a class of strongly interacting $2+1$-dimensional conformal field theories with anti-de Sitter space duals. We obtain these transport coefficients as a function of charge density, background magnetic field, temperature, and frequency. We show that the thermal conductivity and thermoelectric coefficient are determined by the electrical conductivity alone. At small frequency, in the hydrodynamic limit, we are able to provide a number of analytic formulas for the electrical conductivity. A dominant feature of the conductivity is the presence of a cyclotron pole. We show how bulk electromagnetic duality acts on the transport coefficients.

Following the recent trend we develop further the black hole analogy between quantum information theory and the theory of extremal stringy black hole solutions. We show that the three-qubit interpretation of supersymmetric black hole solutions in the $STU$ model can be extended also to include nonsupersymmetric ones. First we show that the black hole potential can be expressed as one half the norm of a suitably chosen three-qubit entangled state containing the quantized charges and the moduli. The extremization of the black hole potential in terms of this entangled state amounts to either suppressing bit flip errors (BPS case) or allowing very special types of flips transforming the states between different classes of non-BPS solutions. We are illustrating our results for the example of the $D2–D6$ system. In this case the bit flip errors are corresponding to sign flip errors of the charges originating from the number of $D2$ branes. After moduli stabilization the states depending entirely on the charges are maximally entangled graph states (of the triangle graph) well known from quantum information theory. An $N=8$ interpretation of the $STU$ model in terms of a mixed state with fermionic purifications is also given.

A five dimensional model containing both left-right and quark-lepton symmetries is constructed, with the gauge group broken by a combination of orbifold compactification and the Higgs mechanism. An analysis of the gauge and scalar sectors is performed and it is shown that the 5D model admits a simpler scalar sector. Bounds on the relevant symmetry breaking scales are obtained and reveal that two neutral gauge bosons may appear in the TeV energy range to be explored by the LHC. Split fermions are employed to remove the mass relations implied by the quark-lepton symmetry and the necessary fermion localization is achieved by introducing bulk scalars with kink vacuum profiles. The symmetries of the model constrain the Yukawa sector, which in turn severely constrains the extent to which realistic split fermion scenarios may be realized in the absence of Yukawa coupling hierarchies. Nevertheless we present two interesting one generation constructs. One of these provides a rationale for $m_t>m_b,m_{\tau }$ and $m_{\nu }\ll m_t$ with Yukawa parameters which vary by only a factor of 5. The other also suppresses the proton decay rate by spatially separating quarks and leptons but requires a Yukawa parameter hierarchy of order ${10}^2$.

We present a covariant decomposition of Einstein’s field equations which is particularly suitable for perturbations of spherically symmetric—and general locally rotationally symmetric—spacetimes. Based upon the utility of the $1+3$ covariant approach to perturbation theory in cosmology, the semi-tetrad, $1+1+2$ approach presented here should be useful for analyzing perturbations of a variety of systems in a covariant and gauge-invariant manner. Such applications range from stellar objects to cosmological models such as the spherically symmetric Lemaître-Tolman-Bondi solutions or the class of locally rotationally symmetric Bianchi models.

We evaluate the nucleon axial form factor, $G_A(q^2)$, and induced pseudoscalar form factor, $G_p(q^2)$, as well as the pion-nucleon form factor, $G_{\pi NN}(q^2)$, in lattice QCD. We also evaluate the corresponding nucleon to $\Delta$ transition form factors, $C_5^A(q^2)$ and $C_6^A(q^2)$, and the pion-nucleon-$\Delta$ form factor $G_{\pi N\Delta }(q^2)$. The nucleon form factors are evaluated in the quenched theory and with two degenerate flavors of dynamical Wilson fermions. The nucleon to $\Delta$ form factors, besides Wilson fermions, are evaluated using domain wall valence fermions with staggered sea quark configurations for pion masses as low as about 350 MeV. Using these form factors, together with an evaluation of the renormalized quark mass, we investigate the validity of the diagonal and nondiagonal Goldberger-Treiman relations. The ratios $G_{\pi N\Delta }(q^2)/G_{\pi NN}(q^2)$ and $2C_5^A(q^2)/G_A(q^2)$ are constant as a function of the momentum transfer squared and show almost no dependence on the quark mass. We confirm equality of these two ratios consistent with the Goldberger-Treiman relations extracting a mean value of 1.61(2).