We have studied volumes of the 3-cycle and the compact 5-volumes for the $\beta$ transformed geometry and it comes out to be decreasing except one choice for which the torus does not stay inside the 3-cycle and “5-cycle.” There are 3 possible ways to construct these cycles. One is as mentioned above and the other two are when the torus stays inside the cycle and when both the torus and the cycle share a common direction. Also, we have argued that under $\beta$-deformation there arises a nontrivial “potential” as the $SL(3,R)$ transformation mixes up the fields. If we start with a flat space after the $SL(3,R)$ transformation the Ricci scalar of the transformed geometry does not vanish but the transformed solution is reminiscent of the NS5-brane. We have explicitly checked that $\beta$-transformation indeed is a marginal deformation on the gravity side.

Numerical simulations of the approach to the singularity in spacetimes with stiff fluid matter are presented here. The spacetimes examined have no symmetries and can be regarded as representing the general behavior of singularities in the presence of such matter. It is found that the singularity is spacelike and that as it is approached, the spacetime dynamics becomes local and nonoscillatory.

We consider axially symmetric, rotating boson stars. Their flat-space limits represent spinning $Q$-balls. We discuss their properties and determine their domain of existence. $Q$-balls and boson stars are stationary solutions and exist only in a limited frequency range. The coupling to gravity gives rise to a spiral-like frequency dependence of the boson stars. We address the flat-space limit and the limit of strong gravitational coupling. For comparison we also determine the properties of spherically symmetric $Q$-balls and boson stars.

Supersymmetric gauge theories, in higher dimensions compactified in an orbifold, give a natural framework to unify the gauge bosons, Higgs fields, and even the matter fields in a single multiplet of the unifying gauge symmetry. The extra dimensions and the supersymmetry are the two key ingredients for such an unification. In this work, we investigate various scenarios for the unification of the three gauge couplings and the Yukawa couplings in the minimal supersymmetric standard model (MSSM), as well as the trilinear Higgs couplings $\lambda$ and $\kappa$ of the nonminimal supersymmetric standard model (NMSSM). We present an $SU(8)$ model in six dimensions with $N=2$ supersymmetry, compactified in a $T^2/Z_6$ orbifold which unifies the three gauge couplings with $\lambda$ and $\kappa$ of NMSSM. Then we present an $SU(9)$ model in 6D, which, in addition, includes partial unification of Yukawa couplings, either for the up-type (top quark and Dirac tau neutrino) or down-type (bottom quark and tau lepton). We also study the phenomenological implications of these various unification scenarios using the appropriate renormalization group equations and show that such unification works very well with the measured low energy values of the couplings. The predicted upper bounds for the lightest neutral Higgs boson mass in our model is higher than those in MSSM but lower than those in the general NMSSM (where the couplings $\lambda$ and $\kappa$ are arbitrary). Some of the predictions of our models can be tested in the upcoming Large Hadron Collider.

In a dense star, the Pauli exclusion principle functions as an enormous energy storage mechanism. Supersymmetry could provide a way to recapture this energy. If there is a transition to an exactly supersymmetric (SUSY) phase, the trapped energy can be released with consequences similar to gamma ray burst observations. Previous zeroth order calculations have been based on the behavior in a prototypical white dwarf of solar mass and earth radius (such as Sirius B) and have neglected density inhomogeneity. In this article we show that the effects of density inhomogeneity and of variations in masses and radii are substantial enough to encourage further exploration of the SUSY star model. In addition, the effects discussed here have possible applications to the growth of bubbles in other phase transition models in dense matter.

String breaking by dynamical quarks in three-dimensional lattice QCD is analyzed through measurements of the potential and the local color-electric field strength generated by a static quark-antiquark pair. Simulations were done for unquenched SU(2) color with two flavors of staggered light quarks. An improved gluon action was used, which allows simulations to be done on coarse lattices, providing an extremely efficient means to access the large quark separations and long propagation times at which string breaking occurs. The static sources were generated using Wilson loop operators, hence no light valence quarks are present in the resulting trial states. Results give unambiguous evidence of string breaking. First the static potential is shown to saturate at twice the heavy-light meson mass at large separations. Then it is demonstrated that the local color-electric field strength in the region between the heavy quarks tends towards vacuum values at large separations, the first time that this most graphic effect of quark vacuum polarization on the confining flux-tube has been realized in lattice QCD. Implications of these results for unquenched simulations of four-dimensional QCD are drawn.

We consider the class of gauges that interpolates between Landau- and Coulomb-gauge QCD, and show the nonrenormalization of the two independent ghost-gluon vertices. This implies the existence of two renormalization group (RG)-invariant running couplings, one of which is interpreted as an RG-invariant gauge parameter. We also present the asymptotic infrared limit of solutions of the Dyson-Schwinger equations in interpolating gauges. The infrared critical exponents of these solutions as well as the resulting infrared fixed point of one of the couplings are independent of the gauge parameter. This coupling also has a fixed point in the Coulomb-gauge limit and constitutes a second invariant charge besides the well known color-Coulomb potential.

In this article we propose standard model strictly forbidden decay modes, quarkonia ($\overline{Q}{Q}_{1^{--}}=J/\psi ,{\rm Y}$) decays into two photons, as a possible signature of space-time noncommutativity. An experimental discovery of $J/\psi \to \gamma \gamma$ and/or ${\rm Y}\to \gamma \gamma$ processes would certainly indicate a violation of the Landau-Pomeranchuk-Yang theorem and a definitive appearance of new physics.

A quantitative understanding of the weak nuclear response is a prerequisite for the analyses of neutrino experiments such as K2K and MiniBOONE, which measure energy and angle of the muons produced in neutrino-nucleus interactions in the energy range $0.5–3\mathrm{GeV}$ and reconstruct the incident neutrino energy to determine neutrino oscillations. In this paper we discuss theoretical calculations of electron- and neutrino-nucleus scattering, carried out within the impulse approximation scheme using realistic nuclear spectral functions. Comparison between electron scattering data and the calculated inclusive cross section of oxygen, at beam energies ranging between 700 and 1200 MeV, show that the Fermi gas model, widely used in the analysis of neutrino oscillation experiments, fails to provide a satisfactory description of the measured cross sections, and inclusion of nuclear dynamics is needed.

In the Randall-Sundrum scenario, our universe is a 4-dimensional “brane“ living in a 5-dimensional bulk spacetime. By studying the scattering of bulk gravity waves, we show that this brane rings with a characteristic set of complex quasinormal frequencies, much like a black hole. To a bulk observer these modes are interpreted as metastable gravity wave bound states, while a brane observer views them as a discrete spectrum of decaying massive gravitons. Potential implications of these scattering resonances are discussed.

We compare different Polyakov-loop actions yielding effective descriptions of finite-temperature $SU(2)$ Yang-Mills theory on the lattice. The actions are motivated by a simultaneous strong coupling and character expansion obeying center symmetry and include both Ising and Ginzburg-Landau type models. To keep things simple we limit ourselves to nearest-neighbor interactions. Some truncations involving the most relevant characters are studied within a novel mean-field approximation. Using inverse Monte Carlo techniques based on exact geometrical Schwinger-Dyson equations we determine the effective couplings of the Polyakov-loop actions. Monte Carlo simulations of these actions reveal that the mean-field analysis is a fairly good guide to the physics involved. Our Polyakov-loop actions reproduce standard Yang-Mills observables well up to limitations due to the nearest-neighbor approximation.

We study the Casimir force between defects (branes) of codimension larger than 1 due to quantum fluctuations of a scalar field $\varphi$ living in the bulk. We show that the Casimir force is attractive and that it diverges as the distance between the branes approaches a critical value $L_c$. Below this critical distance $L_c$ the vacuum state $\varphi =0$ of the theory is unstable, due to the birth of a tachyon, and the field condenses.

We investigate the dynamics of a boundary field coupled to a bulk field with a linear coupling in an anti-de Sitter bulk spacetime bounded by a Minkowski (Randall-Sundrum) brane. An instability criterion for the coupled boundary and bulk system is found. There exists a tachyonic bound state when the coupling is above a critical value, determined by the masses of the brane and bulk fields and AdS curvature scale. This bound state is normalizable and localized near the brane, and leads to a tachonic instability of the system on large scales. Below the critical coupling, there is no tachyonic state and no bound state. Instead, we find quasinormal modes which describe stable oscillations, but with a finite decay time. Only if the coupling is tuned to the critical value does there exist a massless stable bound state, as in the case of zero coupling for massless fields. We discuss the relation to gravitational perturbations in the Randall-Sundrum brane-world.

We show how the quantum-to-classical transition of the cosmological fluctuations produced during inflation can be described by means of the influence functional and the master equation. We split the inflaton field into the system field (long-wavelength modes), and the environment, represented by its own short-wavelength modes. We compute the decoherence times for the system-field modes and compare them with the other time scales of the model. We present the renormalized stochastic Langevin equation for an homogeneous system field and then we analyze the influence of the environment on the power spectrum for some modes in the system.

We analyze the neutrino events from the supernova (SN) 1987A detected by the Kamiokande-II (KII) and Irvine-Michigan-Brookhaven (IMB) experiments. For the time-integrated flux we assume a quasithermal spectrum of the form $(E/E_0{)}^{\alpha }{e}^{-(\alpha +1)E/E_0}$ where $\alpha$ plays the role of a spectral index. This simple representation not only allows one to fit the total energy $E_{\mathrm{tot}}$ emitted in ${\overline{\nu }}_e$ and the average energy $⟨E_{{\overline{\nu }}_e}⟩$, but also accommodates a wide range of shapes, notably antipinched spectra that are broader than a thermal distribution. We find that the pile-up of low-energy events near threshold in KII forces the best-fit value for $\alpha$ to the lowest value of any assumed prior range. This applies to the KII events alone as well as to a common analysis of the two data sets. The preference of the data for an “unphysical” spectral shape implies that one can extract meaningful values for $⟨E_{{\overline{\nu }}_e}⟩$ and $E_{\mathrm{tot}}$ only if one fixes a prior value for $\alpha$. The tension between the KII and IMB data sets and theoretical expectations for $⟨E_{{\overline{\nu }}_e}⟩$ is not resolved by an antipinched spectrum.

We perform a search for gravitational wave bursts using data from the second science run of the LIGO detectors, using a method based on a wavelet time-frequency decomposition. This search is sensitive to bursts of duration much less than a second and with frequency content in the 100–1100 Hz range. It features significant improvements in the instrument sensitivity and in the analysis pipeline with respect to the burst search previously reported by LIGO. Improvements in the search method allow exploring weaker signals, relative to the detector noise floor, while maintaining a low false alarm rate, $O(0.1)$ $\mu \mathrm{Hz}$. The sensitivity in terms of the root-sum-square (rss) strain amplitude lies in the range of $h_{\mathrm{rss}}\sim {10}^{-20}-{10}^{-19}{\mathrm{Hz}}^{-1/2}$. No gravitational wave signals were detected in 9.98 days of analyzed data. We interpret the search result in terms of a frequentist upper limit on the rate of detectable gravitational wave bursts at the level of 0.26 events per day at 90% confidence level. We combine this limit with measurements of the detection efficiency for selected waveform morphologies in order to yield rate versus strength exclusion curves as well as to establish order-of-magnitude distance sensitivity to certain modeled astrophysical sources. Both the rate upper limit and its applicability to signal strengths improve our previously reported limits and reflect the most sensitive broad-band search for untriggered and unmodeled gravitational wave bursts to date.

Supernovae searches have shown that a simple matter-dominated and decelerating universe should be ruled out. However, a determination of the present deceleration parameter $q_0$ through a simple kinematical description is not exempt of possible drawbacks. We show that, with a time dependent equation of state for the dark energy, a bias is present for $q_0$: models which are very far from the so-called concordance model can be accommodated by the data, and a simple kinematical analysis can lead to wrong conclusions. We present a quantitative treatment of this bias and we present our conclusions when a possible dynamical dark energy is taken into account.

Using the coupled cluster expansion with the random phase approximation, we calculate the long wavelength vacuum wave function and the vacuum state energy of $2+1$ dimensional Hamiltonian SU(2) lattice gauge theory up to the seventh order. The coefficients ${\mu }_0$, ${\mu }_2$ of the vacuum wave function show good scaling behavior and convergence in high order calculations.

Plasma instabilities can play a fundamental role in plasma equilibration. There are similarities and differences between plasma instabilities in Abelian and non-Abelian gauge theories. In particular, it has been an open question whether non-Abelian self-interactions are the limiting factor in the growth of non-Abelian plasma instabilities. We study this problem with $3+1$ dimensional numerical simulations. We find that non-Abelian plasma instabilities behave very differently from Abelian ones once they grow to be nonperturbatively large, in contrast with earlier results of $1+1$ dimensional simulations. In particular, they grow more slowly at late times, with linear rather than exponential dependence of magnetic energy on time.