We study moduli stabilization and a realization of de Sitter vacua in generalized $F$-term uplifting scenarios of the Kachru-Kallosh-Linde-Trivedi–type anti–de Sitter vacuum, where the uplifting sector $X$ directly couples to the light Kähler modulus $T$ in the superpotential through, e.g., stringy instanton effects. $F$-term uplifting can be achieved by a spontaneous supersymmetry breaking sector, e.g., the Polonyi model, the O’Raifeartaigh model, and the Intriligator-Seiberg-Shih model. Several models with the $X\mathrm{\text{−}}T$ mixing are examined, and qualitative features in most models even with such mixing are almost the same as those in the Kachru-Kallosh-Linde-Trivedi scenario. One of the quantitative changes, which are relevant to the phenomenology, is a larger hierarchy between the modulus mass $m_T$ and the gravitino mass $m_{3/2}$, i.e., $m_T/m_{3/2}=\mathcal{O}(a^2)$, where $a\sim 4{\pi }^2$. In spite of such a large mass, the modulus $F$ term is suppressed not like $F^T=\mathcal{O}(m_{3/2}/a^2)$, but like $F^T=\mathcal{O}(m_{3/2}/a)$ for $\ln (M_{\mathrm{Pl}}/m_{3/2})\sim a$, because of an enhancement factor coming from the $X\mathrm{\text{−}}T$ mixing. Then we typically find a mirage-mediation pattern of gaugino masses of $\mathcal{O}(m_{3/2}/a)$, while the scalar masses would be generically of $\mathcal{O}(m_{3/2})$.

We study a five-dimensional perfect fluid coupled with Kaluza-Klein gravity. By dimensional reduction, a modified form of Maxwell’s equation is obtained, which is relevant to the equation of state of the source. Since the relativistic magnetohydrodynamics and the three-dimensional formulation are widely used to study space matter, we derive the modified Maxwell’s equations and relativistic magnetohydrodynamics in $3+1$ form. We then take an ideal Fermi gas as an example to study the modified effect, which can be visible under high-density or high-energy conditions, while the traditional Maxwell’s equation can be regarded as a result in the low density and low temperature limit. We also indicate the possibility to test the state-relevant effect of Kaluza-Klein theory in a telluric laboratory.

Centered finite volume methods are considered in the context of numerical relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be interpreted as an “adaptive viscosity” modification of centered finite difference algorithms. These points are fully confirmed by one-dimensional black hole simulations. In the three-dimensional case, evidence is found that the use of a conformal decomposition is a key ingredient for the robustness of black hole numerical codes.

We study D-brane inflation in a warped conifold background that includes brane-position dependent corrections for the nonperturbative superpotential. Instead of stabilizing the volume modulus $\chi$ at instantaneous minima of the potential and studying the inflation dynamics with an effective single field (radial distance between a brane and an antibrane) $\varphi$, we investigate the multifield inflation scenario involving these two fields. The two-field dynamics with the potential $V(\varphi ,\chi )$ in this model is significantly different from the effective single-field description in terms of the field $\varphi$ when the field $\chi$ is integrated out. The latter picture underestimates the total number of e-foldings even by 1 order of magnitude. We show that a correct single-field description is provided by a field $\psi$ obtained from a rotation in the two-field space along the background trajectory. This model can give a large number of e-foldings required to solve flatness and horizon problems at the expense of fine-tunings of model parameters. We also estimate the spectra of density perturbations and show that the slow-roll parameter ${\eta }_{\psi \psi }=M_{\mathrm{pl}}^2{V}_{,\psi \psi }/V$ in terms of the rotated field $\psi$ determines the spectral index of scalar metric perturbations. We find that it is generally difficult to satisfy, simultaneously, both constraints of the spectral index and the cosmic background explorer normalization, while the tensor to scalar ratio is sufficiently small to match with observations.

In light of recent findings which seem to disfavor a scenario with (warm) dark matter entirely constituted of sterile neutrinos produced via the Dodelson-Widrow mechanism, we investigate the constraints attainable for this mechanism by relaxing the usual hypothesis that the relic neutrino abundance must necessarily account for all of the dark matter. We first study how to reinterpret the limits attainable from x-ray nondetection and Lyman-$\alpha$ forest measurements in the case that sterile neutrinos constitute only a fraction $f_s$ of the total amount of dark matter. Then, assuming that sterile neutrinos are generated in the early universe solely through the Dodelson-Widrow mechanism, we show how the x-ray and Lyman-$\alpha$ results jointly constrain the mass-mixing parameters governing their production. Furthermore, we show how the same data allow us to set a robust upper limit $f_s\lesssim 0.7$ at the $2\sigma$ level, rejecting the case of dominant dark matter ($f_s=1$) at the $\sim 3\sigma$ level.

We investigate the cosmological signatures of instantons mediating tunneling between de Sitter minima. For generic potentials the Coleman-de Luccia instanton does not necessarily exist; when it does not, the instanton which contributes to the decay rate is the trivial constant solution, known as the Hawking-Moss instanton. With the aid of a toy model we interpret this solution and describe the resulting cosmology. In neither the Coleman-de Luccia nor Hawking-Moss case can the resulting cosmology be closed. An observation of significant positive curvature would therefore rule out the possibility that our universe arose from any transition from a neighboring minimum in the string-theory landscape.

We explore a model for a fermionic dark matter particle family which decouples from the rest of the particles when at least all standard model particles are in equilibrium. We calculate the allowed ranges for mass and chemical potential to be compatible with big bang nucleosynthesis (BBN) calculations and WMAP data for a flat universe with dark energy (${\Omega }_{\Lambda }^0=0.72$, ${\Omega }_M^0=0.27$, $h=0.7$). Futhermore we estimate the free streaming length for fermions and antifermions to allow comparison to large scale structure data (LSS). We find that for dark matter decoupling when all standard model particles are present even the least restrictive combined BBN calculation and WMAP results allow us to constrain the initial dark matter chemical potential to a highest value of 6.3 times the dark matter temperature. In this case, the resulting mass range is at most $1.8\mathrm{eV}\le m\le 53\mathrm{eV}$, where the upper bound scales linearly with $g_{\mathrm{eff}}^s(T_{\mathrm{Dec}})$. From LSS we find that, similar to ordinary warm dark matter models, the particle mass has to be larger than $\sim 500\mathrm{eV}$ [meaning $g_{\mathrm{eff}}^s(T_{\mathrm{Dec}})>{10}^3$] to be compatible with observations of the Ly $\alpha$ forest at high redshift, but still the dark matter chemical potential over temperature ratio can exceed unity.

It is shown that gravitating magnetic fields affect the evolution of curvature perturbations in a way that is reminiscent of a pristine nonadiabatic pressure fluctuation. The gauge-invariant evolution of curvature perturbations is used to constrain the magnetic power spectrum. Depending on the essential features of the thermodynamic history of the Universe, the explicit derivation of the bound is modified. The theoretical uncertainty in the constraints on the magnetic energy spectrum is assessed by comparing the results obtained in the case of the conventional thermal history with the estimates stemming from less conventional (but phenomenologically allowed) post-inflationary evolutions.

We consider the nonminimally coupled $\lambda {\phi }^4$ scalar field theory in de Sitter space and construct the renormalization group improved renormalized effective theory at the one-loop level. Based on the corresponding quantum Friedmann equation and the scalar field equation of motion, we calculate the quantum radiative corrections to the scalar spectral index $n_s$, gravitational wave spectral index $n_g$, and the ratio $r$ of tensor-to-scalar perturbations. When compared with the standard (tree-level) values, we find that the quantum contributions are suppressed by $\lambda N^2$, where $N$ denotes the number of $e$-foldings. Hence, there is an $N^2$ enhancement with respect to the naive expectation, which is due to the infrared enhancement of scalar vacuum fluctuations characterizing de Sitter space. Since observations constrain $\lambda$ to be very small $\lambda \sim {10}^{-12}$ and $N\sim 50–60$, the quantum corrections in this inflationary model are unobservably small.

We perform a lattice Monte Carlo calculation of the two-point functions of the energy-momentum tensor at finite temperature in the SU(3) gauge theory. Unprecedented precision is obtained thanks to a multilevel algorithm. The lattice operators are renormalized nonperturbatively and the classical discretization errors affecting the correlators are corrected for. A conservative upper bound for the shear viscosity to entropy density ratio is derived, $\eta /s<1.0$, and our best estimate is $\eta /s=0.134(33)$ at $T=1.65T_c$ under the assumption of smoothness of the spectral function in the low-frequency region.

We use the chiral quark soliton model to estimate masses and widths of the two eikosiheptaplets (27-plets of SU(3) flavor) of spin $3/2$ and $1/2$ that emerge in the rigid rotator quantization. We use as input: hyperon decays, ${\Theta }^{+}$ mass, and width. While ${27}_{3/2}$ has small widths (although much larger than the values allowed by the partial wave analysis), ${27}_{1/2}$ has large decay widths to antidecuplet. However, exactly for this decay channel the widths are suppressed in the large $N_c$ limit.

We discuss the results of a search for anomaly-free Abelian ${\mathbb{Z}}_N$ discrete symmetries that lead to automatic R-parity conservation and prevent dangerous higher-dimensional proton decay operators in simple extensions of minimal supersymmetric extension of the standard model based on the left-right symmetric group, the Pati-Salam group and SO(10). We require that the superpotential for the models have enough structures to be able to give correct symmetry breaking to minimal supersymmetric extension of the standard model and potentially realistic fermion masses. We find viable models in each of the extensions, and for all the cases, anomaly freedom of the discrete symmetry restricts the number of generations.

In the past several decades there have been a number of proposals for computing with dual forms of non-Abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful applications of duality in the $U(1)$ case, we revisit the question of whether it is practical to perform numerical computation using non-Abelian dual models. Specifically, we consider three-dimensional $SU(2)$ pure Yang-Mills as an accessible yet nontrivial case in which the gauge group is non-Abelian. Using methods developed recently in the context of spin foam quantum gravity, we derive an algorithm for efficiently computing the dual amplitude and describe Metropolis moves for sampling the dual ensemble. We relate our algorithms to prior work in non-Abelian dual computations of Hari Dass and his collaborators, addressing several problems that have been left open. We report results of spin expectation value computations over a range of lattice sizes and couplings that are in agreement with our conventional lattice computations. We conclude with an outlook on further development of dual methods and their application to problems of current interest.

We study neutrino emission from direct Urca processes in pion condensed quark matter. In compact stars with high baryon density, the emission is dominated by the gapless modes of the pion condensation which leads to an enhanced emissivity. While for massless quarks the enhancement is not remarkable, the emissivity is significantly larger and the cooling of the condensed matter is considerably faster than that in normal quark matter when the mass difference between $u$ and $d$ quarks is sizable.

The fundamental theory of nature may allow a large landscape of vacua. Even if the theory contains a unified gauge symmetry, the 22 flavor parameters of the standard model, including neutrino masses, may be largely determined by the statistics of this landscape, and not by any symmetry. Then the measured values of the flavor parameters do not lead to any fundamental symmetries, but are statistical accidents; their precise values do not provide any insights into the fundamental theory, rather the overall pattern of flavor reflects the underlying landscape. We investigate whether random selection from the statistics of a simple landscape can explain the broad patterns of quark, charged lepton, and neutrino masses and mixings. We propose Gaussian landscapes as simplified models of landscapes where Yukawa couplings result from overlap integrals of zero-mode wave functions in higher-dimensional supersymmetric gauge theories. In terms of just five free parameters, such landscapes can account for all gross features of flavor, including the hierarchy of quark and charged-lepton masses; small quark mixing angles in the basis with quarks arranged according to mass, with 13 mixing less than 12 and 23 mixing; very light Majorana neutrino masses, with the solar to atmospheric neutrino mass ratio consistent with data; distributions for leptonic mixings $\sin 2{\theta }_{12}$ and $\sin 2{\theta }_{23}$ that are peaked at large values, while the distribution for $\sin 2{\theta }_{13}$ is peaked at low values; and order unity $CP$-violating phases in both the quark and lepton sectors. While the statistical distributions for flavor parameters are broad, the distributions are robust to changes in the geometry of the extra dimensions. Constraining the distributions by loose cuts about observed values leads to narrower distributions for neutrino measurements of ${\theta }_{13}$, $CP$ violation, and neutrinoless double beta decay.

We report results from a search for the decay $B_s^0\to {\mu }^{+}{\mu }^{-}$ using $1.3{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected by the D0 experiment at the Fermilab Tevatron Collider. We find two candidate events, consistent with the expected background of $1.24\pm 0.99$, and set an upper limit on the branching fraction of $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-})<1.2\times {10}^{-7}$ at the 95% C.L.

We solve systematically for the right-handed quark mixings in the minimal left-right symmetric model which generally has both explicit and spontaneous $CP$ violations. The leading-order result has the same hierarchical structure as the left-handed Cabibbo-Kobayashi-Maskawa mixing, but with additional $CP$ phases originating from a spontaneous $CP$-violating phase in the Higgs vacuum expectation values. We explore the phenomenology entailed by the new right-handed mixing matrix, particularly the bounds on the mass of $W_R$ and the $CP$ phase of the Higgs vacuum expectation values.

We consider flux compactifications of type IIB string theory on the mirror of a rigid Calabi-Yau. In special cases, these models are dual to the type IIA flux vacua with runaway direction in flux space. We show that new weak coupling AdS solutions can be found for large complex structure, while Minkowski solutions with all moduli stabilized are confined to be at strong coupling. The existence of these solutions, as found in a previous work, is nevertheless guaranteed by a nonrenormalization theorem of the type IIB flux superpotential. Based on our results, we are led to the conjecture that supersymmetric runaway directions in flux space are always accompanied by a spectrum of moduli masses reaching down to the AdS scale. This could be violated in a nonsupersymmetric situation.

We study Bogomol’nyi-Prasad-Sommerfield (BPS) non-Abelian semilocal vortices in $U(N_{\mathrm{C}})$ gauge theory with $N_{\mathrm{F}}$ flavors, $N_{\mathrm{F}}>N_{\mathrm{C}}$, in the Higgs phase. The moduli space for an arbitrary winding number is described using the moduli matrix formalism. We find a relation between the moduli spaces of the semilocal vortices in Seiberg-like dual pairs of theories, $U(N_{\mathrm{C}})$ and $U(N_{\mathrm{F}}-N_{\mathrm{C}})$. They are two alternative regularizations of a parent non-Hausdorff space, which tend to the same moduli space of sigma model lumps in the infinite gauge coupling limits. We examine the normalizability of the zero-modes and find the somewhat surprising phenomenon that the number of normalizable zero-modes, dynamical fields in the effective action, depends on the point of the moduli space we are considering. We find, in the lump limit, an effective action on the vortex world sheet, which we compare to that found by Shifman and Yung.

The recursion relations of hierarchical models are studied and contrasted with functional renormalization group equations in corresponding approximations. The formalisms are compared quantitatively for the Ising universality class, where the spectrum of universal eigenvalues at criticality is studied. A significant correlation amongst scaling exponents is pointed out and analyzed in view of an underlying optimization. Continuous functional flows are provided which match with high accuracy all known scaling exponents from Dyson’s hierarchical model for discrete block-spin transformations. Implications of the results are discussed.