The constraints of gauge unification on intermediate mass scales in nonsupersymmetric $SO(10)$ scenarios are systematically discussed. With respect to the existing reference studies we include the $U(1)$ gauge mixing renormalization at the one- and two-loop level, and reassess the two-loop beta coefficients. We evaluate the effects of additional Higgs multiplets required at intermediate stages by a realistic mass spectrum and update the discussion to the present day data. On the basis of the obtained results, $SO(10)$ breaking patterns with up to two intermediate mass scales are discussed for potential relevance and model predictivity.

It is shown that the low energy coefficients of the next-to-leading order chiral perturbation theory needed to determine the physical $\Delta I=1/2$, $K\to \pi \pi$ decay amplitude can be fixed by calculating $K\pi \to \pi$ amplitudes on the lattice. Unlike using next-to-leading order $K\to \pi \pi$ amplitudes proposed by Laiho and Soni, simulating $K\pi \to \pi$ transitions on the lattice does not require evaluations of $s$-channel disconnected diagrams which have been an obstacle in practice.

We calculate the equation of state in $2+1$ flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent $N_{\tau }=8$. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two $O(a^2)$ improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on $N_{\tau }=6$ and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we include an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects.

Using the same quenched limit as input, we compare the charmonium spectra predicted by two different models, i.e., the coupled-channel model and the screened potential model in the mass region below 4 GeV, in which the contributions from decay channels involving $P$-wave (as well as even higher excited) $D$ mesons can be neglected. We find that the two models have similar global features in describing the charmonium spectrum since they approximately embody the same effect of the vacuum polarization of dynamical light quark pairs. Adopting these models will be helpful to clarify the nature of the newly discovered charmonium or charmoniumlike states; and the coupled-channel model is more adept in investigating the influences of open-charm thresholds on the charmonium spectrum. In particular, we show the $S$-wave decay coupling effect on lowering the ${\chi }_{c1}(2P)$ mass toward the $D{\overline{D}}^{*}$ threshold, in support of the assignment of the $X(3872)$ as a ${\chi }_{c1}(2P)$-dominated charmonium state.

The quantized charges $x$ of four-dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding $U$ duality and whose $U$-invariant quartic norm $\Delta (x)$ determines the lowest-order entropy. Here, we introduce a Freudenthal duality $x\to \tilde{x}$, for which $\tilde{\tilde{x}}=-x$. Although distinct from $U$ duality, it nevertheless leaves $\Delta (x)$ invariant. However, the requirement that $\tilde{x}$ be an integer restricts us to the subset of black holes for which $\Delta (x)$ is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete $U$-duality invariants are Freudenthal invariant. Similarly, the quantized charges $A$ of five-dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm $N(A)$ determines the lowest-order entropy. We introduce an analogous Jordan dual $A^{\star }$, with $N(A)$ necessarily a perfect cube, for which $A^{\star \star }=A$ and which leaves $N(A)$ invariant. The two dualities are related by a $4\mathrm{D}/5\mathrm{D}$ lift.

We study BPS vortices in the mass-deformed nonrelativistic $\mathcal{N}=6$ $U(N{)}_k\times U(N{)}_{-k}$ Chern-Simons-matter theory. We focus on the massive deformation that preserves the maximal $\mathcal{N}=6$ supersymmetry and consider a nonrelativistic limit that carries 14 supercharges. In this nonrelativistic field theory we find Jackiw-Pi type exact vortex solutions combined with $S^3$ fuzzy sphere geometry. We analyze their properties and show that they preserve one dynamical, one conformal, and five kinematical supersymmetries among the full super Schrödinger symmetry.

We introduce the domain structure for stationary black hole space-times. The domain structure lives on the submanifold of fixed points of the Killing vector fields. Depending on which Killing vector field has fixed points the submanifold is naturally divided into domains. The domain structure provides invariants of the space-time, both topological and continuous. It is defined for any space-time dimension and any number of Killing vector fields. We examine the domain structure for asymptotically flat space-times and find a canonical form for the metric of such space-times. The domain structure generalizes the rod structure introduced for space-times with $D-2$ commuting Killing vector fields. We analyze in detail the domain structure for Minkowski space, the Schwarzschild-Tangherlini black hole and the Myers-Perry black hole in six and seven dimensions. Finally, we consider the possible domain structures for asymptotically flat black holes in six and seven dimensions.

We reformulate an approach fist given by Barbour and Bertotti (BB) for implementing Mach’s principle for nonrelativistic particles. This reformulation can deal with arbitrary symmetry groups and finite group elements. Applying these techniques to U(1) and SU(N) invariant scalar field theories, we show that BB’s proposal is nearly equivalent to defining a covariant derivative using a dynamical connection. We then propose a modified version of the BB method which implements Mach’s principle using gauge theory techniques and argue that this modified method is equivalent to the original. Given this connection between the particle models and Yang-Mills theories, we consider the effect of dynamic curvature as a possible generalization of the BB scheme. Since the BB method can be used as a novel way of deriving geometrodynamics, the connection with gauge theory may shed new light on the gauge properties of the gravitational field.

We consider a family of spherical three-dimensional spacelike slices embedded in the Schwarzschild solution. The mean curvature is constant on each slice but can change from slice to slice. We give a simple expression for an everywhere positive lapse and thus we show how to construct foliations. There is a barrier preventing the mean curvature from becoming large, and we show how to avoid this so as to construct a foliation where the mean curvature runs all the way from zero to infinity. No foliation exists where the mean curvature goes from minus to plus infinity. There are slicings, however, where each slice passes through the bifurcation sphere $R=2M$ and the lapse only vanishes at this one point, and is positive everywhere else, while the mean curvature does run from minus to plus infinity. Symmetric foliations of the extended Schwarzschild spacetime degenerate at a critical point, where we show that the lapse function exponentially approaches zero.

We consider the early time cosmology of $f(R)$ theories in Palatini formalism and study the conditions that guarantee the existence of homogeneous and isotropic models that avoid the big bang singularity. We show that for such models the big bang singularity can be replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for pressureless dust. We give a characterization of such models and discuss their dynamics in the region near the bounce. We also find that power-law Lagrangians with a finite number of terms may lead to nonsingular universes, which contrasts with the infinite-series Palatini $f(R)$ Lagrangian that one needs to fully capture the effective dynamics of loop quantum cosmology. We argue that these models could also avoid the formation of singularities during stellar gravitational collapse.

We consider the signals of indirect dark matter detection resulting from a theory of two universal extra dimensions compactified on a chiral square. Aside from the continuum emission, which is a generic prediction of most dark matter candidates, we find a series of prominent annihilation lines (a WIMP forest) that, after convolution with the angular resolution of current experiments, leads to a distinctive (2-bump plus continuum) spectrum, which may be visible in the near future with the Fermi Gamma-Ray Space Telescope (formerly known as GLAST).

We explore the available parameter space of the minimal vectorial standard model. In this theory, the gauge currents are initially vectorial but the Higgs sector produces chiral mass eigenstates, leading to a set of heavy right-handed mirror particles. We describe the phenomenology of the residual parameter space and suggest that the model will be readily tested at the LHC.

Motivated in part by the several observed anomalies involving $CP$ asymmetries of $B$ and $B_s$ decays, we consider the standard model with a 4th sequential family (SM4) which seems to offer a rather simple resolution. We initially assume $T$-invariance by taking the up and down-quark $4\times 4$ mass matrix to be real. Following Friedberg and Lee (FL), we then impose a hidden symmetry on the unobserved (hidden) up and down-quark SU(2) states. The hidden symmetry for four generations ensures the existence of two zero-mass eigenstates, which we take to be the $(u,c)$ and $(d,s)$ states in the up and down-quark sectors, respectively. Then, we simultaneously break $T$-invariance and the hidden symmetry by introducing two phase factors in each sector. This breaking mechanism generates the small quark masses $m_u$, $m_c$ and $m_d$, $m_s$, which, along with the orientation of the hidden symmetry, determine the size of $CP$-violation in the SM4. For illustration we choose a specific physical picture for the hidden symmetry and the breaking mechanism that reproduces the observed quark masses, mixing angles and $CP$-violation, and at the same time allows us to further obtain very interesting relations/predictions for the mixing angles of $t$ and $t^{\prime }$. For example, with this choice we get $V_{td}\sim (V_{cb}/V_{cd}-V_{ts}/V_{us})+\mathcal{O}({\lambda }^2)$ and $V_{t^{\prime }b}\sim V_{t^{\prime }d}·(V_{cb}/V_{cd})$, $V_{t{b}^{\prime }}\sim V_{t^{\prime }d}·(V_{ts}/V_{us})$, implying that $V_{t^{\prime }d}>V_{t^{\prime }b}$, $V_{t{b}^{\prime }}$. We furthermore find that the Cabibbo angle is related to the orientation of the hidden symmetry and that the key $CP$-violating quantity of our model at high energies, $J_{\mathrm{SM}4}\equiv \mathrm{Im}(V_{tb}{V}_{t^{\prime }b}^{\star }{V}_{t^{\prime }{b}^{\prime }}{V}_{t{b}^{\prime }}^{\star })$, which is the high-energy analogue of the Jarlskog invariant of the SM, is proportional to the light-quark masses and the measured Cabibbo-Kobayashi-Maskawa quark-mixing matrix angles: $|J_{\mathrm{SM}4}|\sim A^3{\lambda }^5\times (\sqrt{m_u/m_t}+\sqrt{m_c/m_{t^{\prime }}}-\sqrt{m_d/m_b}+\sqrt{m_s/m_{b^{\prime }}})\sim {10}^{-5}$, where $A\sim 0.81$ and $\lambda =0.2257$ are the Wolfenstein parameters. Other choices for the orientation of the hidden symmetry and/or the breaking mechanism may lead to different physical outcomes. A general solution, obtained numerically, will be presented in a forthcoming paper.

We present numerical solutions of the semiclassical Boltzmann-Vlasov equation for fermion particle-antiparticle production by strong electric fields in boost-invariant coordinates in ($1+1$) and ($3+1$) dimensional QED. We compare the Boltzmann-Vlasov results with those of recent quantum field theory calculations and find good agreement. We conclude that extending the Boltzmann-Vlasov approach to the case of QCD should allow us to do a thorough investigation of how backreaction affects recent results on the dependence of the transverse momentum distribution of quarks and antiquarks on a second Casimir invariant of color SU(3).

We study the fermion pair production from a strong electric field in boost-invariant coordinates in ($3+1$) dimensions and exploit the cylindrical symmetry of the problem. This problem has been used previously as a toy model for populating the central-rapidity region of a heavy-ion collision (when we can replace the electric by a chromoelectric field). We derive and solve the renormalized equations for the dynamics of the mean electric field and current of the produced particles, when the field is taken to be a function only of the fluid proper time $\tau =\sqrt{t^2-z^2}$. We determine the proper-time evolution of the comoving energy density and pressure of the ensuing plasma and the time evolution of suitable interpolating number operators. We find that unlike in $1+1$ dimensions, the energy density $\epsilon$ closely follows the longitudinal pressure. The transverse-momentum distribution of fermion pairs at large momentum is quite different and larger than that expected from the constant field result.

Starting with a covariant spectator quark model developed for the nucleon $N$ and the $\Delta$ in the physical pion mass region, we extend the predictions of the reaction $\gamma N\to \Delta$ to the lattice QCD regime. The quark model includes $S$ and $D$ waves in the quark-diquark wave functions. Within this framework, it is the $D$-wave part in the $\Delta$ wave function that generates nonzero valence contributions for the quadrupole form factors of the transition. Those contributions are however insufficient to explain the physical data, since the pion cloud contributions dominate. To separate the two effects, we apply the model to the lattice regime in a region where the pion cloud effects are negligible and adjust the $D$-state parameters directly to the lattice data. This process allows us to obtain a better determination of the $D$-state contributions. Finally, by adding a simple parametrization of the pion cloud, we establish the connection between the experimental data and the lattice data.

During the last stage of collapse of a compact object into the horizon of events, the potential energy of its surface layer decreases to a negative value below all limits. The energy-conservation law requires an appearance of a positive-valued energy to balance the decrease. We derive the internal-state properties of the ideal gas situated in an extremely strong, ultrarelativistic gravitational field and suggest the application of our result to a compact object with a radius that is slightly larger than or equal to the Schwarzschild gravitational radius. On the surface of the object, we find that the extreme attractivity of the gravity is accompanied with an extremely high internal heat energy. This internal energy implies a correspondingly high pressure, the gradient of which has such a behavior that it can compete with the gravity. In more detail, we find the equation of state in the case when the magnitude of the potential-type energy of constituting gas particles is much larger than their rest energy. This equation appears to be identical with the general relativity condition of the equilibrium between the gravity and pressure gradient. The consequences of the identity are discussed.

The near-horizon limit of the extremal (weakly) isolated horizon is obtained under the Bondi-like coordinates. For the vacuum case, explicit coordinate transformation relating the near-horizon metric under the Bondi-like coordinates and the standard Poincaré-type or global near-horizon metric of the extremal Kerr black hole is found, which shows that the two geometries are the same. Combined with the known thermodynamics of the (weakly) isolated horizon, it is argued that the Kerr/conformal field theory correspondence can be generalized to the case of a large class of nonstationary extremal black holes.