We use ’t Hooft loops of maximal size on finite lattices to calculate the free energy in the sectors of $\mathrm{SU}\left(2\right)\mathrm{}$ Yang-Mills theory with fixed electric flux, as a function of temperature and (spatial) volume. Our results provide evidence for the mass gap. The confinement of electric fluxes in the low temperature phase and their condensation in the high temperature phase are demonstrated. In a surprisingly large scaling window around criticality, the transition is quantitatively well described by universal exponents and amplitude ratios relating the properties of the two phases.

A comparison is made between proposals for the exact three-point function in Liouville quantum field theory and the nonperturbative weak coupling expansion developed long ago by Braaten, Curtright, Ghandour, and Thorn. Exact agreement to the order calculated [i.e., up to and including corrections of order ${O(g}^{10}\left)\right]$ is found.

We consider the maximal supersymmetric pure Yang-Mills theories on six and eight dimensional space. We determine, in a systematic way, all the possible fractions of supersymmetry preserved by the BPS states and present the corresponding “self-dual” BPS equations. In six dimensions the intrinsic one has 1/4 supersymmetry, while in eight dimensions, 1/16, $2/16,\dots ,6/16.$ We apply our results to some explicit BPS configurations of finite or infinite energy on commutative or noncommutative spaces.

We study four-dimensional superconformal field theories coupled to three-dimensional superconformal boundary or defect degrees of freedom. Starting with bulk $\mathcal{N}=2,$ $d=4\mathrm{}$ theories, we construct Abelian models preserving $\mathcal{N}=2,$ $d=3\mathrm{}$ supersymmetry and the conformal symmetries under which the boundary/defect is invariant. We write the action, including the bulk terms, in $\mathcal{N}=2,$ $d=3\mathrm{}$ superspace. Moreover we derive Callan-Symanzik equations for these models using their superconformal transformation properties and show that the beta functions vanish to all orders in perturbation theory, such that the models remain superconformal upon quantization. Furthermore, we study a model with $\mathcal{N}=4\mathrm{}\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ Yang-Mills theory in the bulk coupled to an $\mathcal{N}=4,$ $d=3\mathrm{}$ hypermultiplet on a defect. This model was constructed by DeWolfe, Freedman, and Ooguri, and conjectured to be conformal based on its relation to an AdS configuration studied by Karch and Randall. We write this model in $\mathcal{N}=2,$ $d=3\mathrm{}$ superspace, which has the distinct advantage that nonrenormalization theorems become transparent. Using $\mathcal{N}=4,$ $d=3\mathrm{}$ supersymmetry, we argue that the model is conformal.

The conformally flat families of initial data typically used in numerical relativity to represent boosted black holes are not those of a boosted slice of Schwarzschild spacetime. If such data are used for each black hole in a collision, the emitted radiation will be partially due to the “relaxation” of the individual holes to “boosted Schwarzschild” form. We attempt to compute this radiation by treating the geometry for a single boosted conformally flat hole as a perturbation of a Schwarzschild black hole, which requires the use of second order perturbation theory. In this we attempt to mimic a previous calculation we did for the conformally flat initial data for spinning holes. We find that the boosted black hole case presents additional subtleties, and although one can evolve perturbatively and compute radiated energies, it is much less clear than in the spinning case how useful for the study of collisions are the radiation estimates for the “spurious energy” in each hole. In addition to this we draw some lessons on which frame of reference appears as more favorable for computing black hole collisions in the close limit approximation.

We obtain geodesically complete spacetimes generated by static and rotating magnetic point sources in an Einstein-Maxwell-dilaton theory of the Brans-Dicke type in three dimensions (3D). The theory is specified by three fields, the dilaton $\phi ,$ the graviton $g_{\mu \nu }$ and the electromagnetic field $F^{\mu \nu },$ and two parameters, the cosmological constant $\Lambda <0\mathrm{}$ and the Brans-Dicke parameter ω. For $\omega =\pm \infty ,$ our solution reduces to the magnetic counterpart of the BTZ solution, while the $\omega =0\mathrm{}$ case is equivalent to 4D general relativity with one Killing vector. The source for the magnetic field can be interpreted as composed by a system of two symmetric and superposed electric charges. One of the electric charges is at rest and the other is spinning.

We explore the phenomenology of microscopic black holes in the $S^1{/Z}_2$ Randall-Sundrum (RS) model. We consider the canonical framework in which both gauge and matter fields are confined to the brane and only gravity spills into the extra dimension. The model is characterized by two parameters: the mass of the first massive graviton ${(m}_1),$ and the curvature $1/l$ of the RS anti–de Sitter space. We compute the sensitivities of present and future cosmic ray experiments to black hole mediated events, for a wide range of l and $m_1,$ and compare them with the sensitivities of Fermilab Tevatron runs I and II to higher-dimensional physics. As part of our phenomenological analysis, we examine constraints placed on l by AdS-CFT considerations.

We study the massive scalar wave propagation in the background of a Reissner-Nordström black hole by using numerical simulations. We learn that the value $\mathrm{Mm}$ plays an important role in determining the properties of the relaxation of the perturbation. For $\mathrm{Mm}\ll 1$ the relaxation process depends only on the field parameter and does not depend on the spacetime parameters. For $\mathrm{Mm}\gg 1,$ the dependence of the relaxation on the black hole parameters appears. The bigger the mass of the black hole, the faster the perturbation decays. The difference of the relaxation process caused by the black hole charge Q has also been exhibited.

New nondiagonal $G_2$ inhomogeneous cosmological solutions are presented in a wide range of scalar-tensor theories with a stiff perfect fluid as a matter source. The solutions have no big-bang singularity or any other curvature singularities. The dilaton field and the fluid energy density are regular everywhere, too. The geodesic completeness of the solutions is investigated.

We consider a de Sitter brane-world motivated by the dS/conformal field theory (CFT) correspondence where both the bulk and brane are de Sitter spaces. The brane tension is fixed by holographic RG. The 4D effective action for metric perturbations and 4D graviton correlator are explicitly found. The induced values of cosmological and Newton constants are calculated. The short distance behavior of the graviton correlator (when no brane matter presents) turns out to be significantly stronger than in the case of general relativity. It is shown that quantum brane CFT gives the dominant contribution to the graviton correlator on small scales such as in the brane new world scenario.

The holographic entropy bound is used to estimate the quantum-gravitational discreteness of inflationary perturbations. In the context of scalar inflaton perturbations produced during standard slow-roll inflation, but assuming that horizon-scale perturbations “freeze out” in discrete steps separated by one bit of total observable entropy, it is shown that the Hilbert space of a typical horizon-scale inflaton perturbation is equivalent to that of about ${10}^5$ binary spins—approximately the inverse of the final scalar metric perturbation amplitude, independent of other parameters. Holography thus suggests that in a broad class of fundamental theories, inflationary perturbations carry a limited amount of information (about ${10}^5$ bits per mode) and should therefore display discreteness not predicted by the standard field theory. Some manifestations of this discreteness may be observable in cosmic background anisotropy.

Observational constraints to a large class of decaying vacuum cosmologies are derived using the angular size data of compact radio sources and the latest age estimates of globular clusters. For this class of deflationary $\Lambda \mathrm{}\left(t\right)\mathrm{}$ models, the present value of the vacuum energy density is quantified by a positive β parameter smaller than unity. In the case of milliarcsecond compact radio-sources, we find that the allowed intervals for β and the matter density parameter ${\Omega }_m$ are heavily dependent on the value of the mean projected linear size l. For $l\simeq {20h}^{-1}-{30h}^{-1}\hspace{0.5em}\mathrm{pc},$ the best fit occurs for $\beta \sim 0.58,$ ${\Omega }_{\mathrm{m}}\sim 0.58,$ and $\beta \sim 0.76,$ ${\Omega }_{\mathrm{m}}\sim 0.28,$ respectively. This analysis shows that if one minimizes ${\chi }^2$ for the free parameters l, ${\Omega }_{\mathrm{m}}$ and β, the best fit for these angular size data corresponds to a decaying $\Lambda \mathrm{}\left(t\right)\mathrm{}$ with ${\Omega }_{\mathrm{m}}=0.54,$ $\beta =0.6,$ and ${l=22.64h}^{-1}$ pc. Constraints from age estimates of globular clusters and old high redshift galaxies are not so restrictive, thereby suggesting that there is no age crisis for this kind of $\Lambda \mathrm{}\left(t\right)\mathrm{}$ cosmologies.

We study the inner magnetohydrodynamic structure of a general relativistic magnetized star, with poloidal and toroidal fields. The star is taken to be differentially rotating, stationary, axisymmetric, and made from perfect, infinitely conducting fluid. Strong toroidal fields of up to ${10}^{17}\hspace{0.5em}\mathrm{G}$ can be created from the initial poloidal field by a variation of the mechanism proposed by Meier et al. and Kluźniak and Ruderman. It is also found that the redshifted toroidal field and the redshifted chemical potential are constants along a magnetic surface. We prove that a spacetime containing an ideal magnetohydrodynamic fluid which flows only azimuthally is circular in the sense of Carter if, and only if, the magnetic field has only poloidal or only toroidal components. Further, we show through post Newtonian analysis that, even when this criterion is breached, spacetime inside astrophysical compact objects where the magnetic field is less than ${10}^{19}\hspace{0.5em}\mathrm{G}$ can be considered circular. In both cases the metric inside the star assumes a simple form, with only one nonvanishing off diagonal term. It is shown that imposing chemical equilibrium forces the magnetic field to assume a force-free configuration. We derive the form of the electric 4-current in force-free relativistic magnetohydrodynamics. The connection between both field components is then given through the vector potential and is used to rule out some field configurations. We derive a new separability condition on the metric which shows that not every pure fluid metric can be dressed with a frozen in, force-free field.

We describe the in-medium properties of hadrons in dense matter near chiral restoration using a Wilsonian matching to QCD of an effective field theory with hidden local symmetry at the chiral cutoff $\Lambda .$ We find that chiral symmetry is restored in vector manifestation in the manner of Harada and Yamawaki at a critical matter density $n_c.$ We express the critical density in terms of QCD correlators in dense matter at the matching scale. In a manner completely analogous to what happens at the critical $N_f^c$ and at the critical temperature $T_c,$ the vector meson mass is found to vanish (in the chiral limit) at chiral restoration. This result provides support for the Brown-Rho scaling predicted a decade ago.

Octet baryon magnetic moments are calculated in the framework of the light cone QCD sum rules. The analysis is carried out for the general form of the interpolating currents for octet baryons. A comparison of our results on the magnetic moments of octet baryons with the predictions of other approaches and experimental data is presented.

The one-loop supersymmetric (SUSY) QCD radiative correction to the $g\overrightarrow{b}{\mathrm{tH}}^{-}$ cross section is calculated in the minimal supersymmetric standard model. We find that SUSY QCD is nondecoupling if the gluino mass and the parameters $\mu ,$ $A_t,$ and $A_b$ are of the same order and get large. The nondecoupling contribution can be enhanced by large $\tan \beta$ and therefore large corrections to the hadronic production rates at the Fermilab Tevatron and CERN Large Hadron Collider (LHC) are expected in the large $\tan \beta$ limit. The fundamental reason for such nondecoupling behavior is that some couplings in the loops are proportional to the SUSY mass parameters.

Many types of physics beyond the standard model include an extended electroweak gauge group. If these extensions are associated with flavor symmetry breaking, the gauge interactions will not be flavor universal. In this paper we update the bounds placed by electroweak data on the existence of flavor nonuniversal extensions to the standard model in the context of top-color assisted technicolor (TC2), noncommuting extended technicolor (NCETC), and the ununified standard model (UUM). In the first two cases the extended gauge interactions couple to the third generation fermions differently than to the light fermions, while in the ununified standard model the gauge interactions couple differently to quarks and leptons. The extra $\mathrm{SU}\left(2\right)\mathrm{}$ triplet of gauge bosons in NCETC and UUM models must be heavier than about 3 TeV, while the extra Z boson in TC2 models must be heavier than about 1 TeV.

A calculus for the derivatives of the eigenvalues of the neutralino mass matrix with respect to the $\mathrm{CP}$ violating background fields is developed and used to compute the mixings among the $\mathrm{CP}$ even and the $\mathrm{CP}$ odd Higgs sectors arising from the inclusion of the neutralino sector consisting of the neutralino, the Z boson, and the neutral Higgs bosons $\left({\chi }_i^0-Z-h^0-H^0\right)$ exchange in the loop contribution to the effective potential including the effects of large $\mathrm{CP}$ violating phases. Along with the top squark, bottom squark, tau slepton and chargino–$W$–charged-Higgs-boson $\left({\chi }^{+}-W-H^{+}\right)$ contributions computed previously the present analysis completes the one loop corrections to the Higgs boson mass matrix in the presence of large phases. $\mathrm{CP}$ violation in the neutral Higgs sector is discussed in the above framework with specific focus on the mixings of the $\mathrm{CP}$ even and the $\mathrm{CP}$ odd sectors arising from the neutralino sector. It is shown that numerically the effects of the neutralino exchange contribution on the mixings of the $\mathrm{CP}$ even and the $\mathrm{CP}$ odd sectors are comparable to the effects of the top squark and of the chargino exchange contributions and thus the neutralino exchange contribution must be included for a realistic analysis of mixings in the $\mathrm{CP}$ even and the $\mathrm{CP}$ odd sectors. Phenomenological implications of these results are discussed.

We develop a new method in lattice QCD to calculate the form factor ${\mathcal{F}}_{\overrightarrow{B}{D}^{*}}\mathrm{}\left(1\right)\mathrm{}$ at zero recoil. This is the main theoretical ingredient needed to determine $|V_{\mathrm{cb}}|$ from the exclusive decay $\overline{B}\to D^{*}l\overline{\nu }.$ We introduce three ratios, in which most of statistical and systematic error cancels, making a precise calculation possible. We fit the heavy-quark mass dependence directly, and extract the ${1/m}_Q^2$ and three of the four ${1/m}_Q^3$ corrections in the heavy-quark expansion. In this paper we show how the method works in the quenched approximation, obtaining ${\mathcal{F}}_{\overrightarrow{B}{D}^{*}}{\mathrm{}\left(1\right)=0.913\mathrm{}}_{-0.017}^{+0.024\mathrm{}}\pm {0.016}_{-0.014-0.016-0.014}^{+0.003+0.000+0.006\mathrm{}}$ where the uncertainties come, respectively, from statistics and fitting, matching lattice gauge theory to QCD, lattice spacing dependence, light quark mass effects, and the quenched approximation. We also discuss how to reduce these uncertainties and, thus, to obtain a model-independent determination of $|V_{\mathrm{cb}}|.$

The mass spectrum of charmed and bottom baryons is computed on anisotropic lattices using quenched lattice nonrelativistic QCD. The masses are extracted by using mass splittings which are more accurate than masses obtained directly by using the nonrelativistic mass-energy relation. Of particular interest are the mass splittings between spin-1/2 and spin-3/2 heavy baryons, and we find that these color hyperfine effects are not suppressed in the baryon sector although they are known to be suppressed in the meson sector. The results are compared with those obtained in a previous nonrelativistic QCD calculation and with those obtained from a Dirac-Wilson action of the D234 type.