The low energy dynamics of degenerated Bogomol’nyi-Prasad-Sommerfield domain walls arising in a generalized Wess-Zumino model is described as geodesic motion in the space of these topological walls.

A semiclassical string description is given for correlators of Wilson loops with local operators in $\mathcal{N}=4\mathrm{}$ supersymmetric Yang-Mills theory in the regime when operators carry a parametrically large R charge. The operator product expansion coefficients of the circular Wilson loop in chiral primary operators are computed to all orders in the ${\alpha }^{\prime }$ expansion in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ string theory. The results agree with field-theory predictions.

The renormalization group flow equation obtained by means of a proper time regulator is used to calculate the two loop $\beta$ function and anomalous dimension $\eta$ of the field for the $O\left(N\right)\mathrm{}$ symmetric scalar theory. The standard perturbative analysis of the flow equation does not yield the correct results for both $\beta$ and $\eta .$ We also show that it is still possible to extract the correct $\beta$ and $\eta$ from the flow equation in a particular limit of the infrared scale. A modification of the derivation of the exact renormalization group flow, which involves a more general class of regulators, to recover the proper time renormalization group flow is analyzed.

In cosmological models with a varying gravitational constant, it is not clear whether primordial black holes preserve the value of G at their formation epoch. We investigate this question by using the Tolman-Bondi model to study the evolution of a background scalar field when a black hole forms from the collapse of dust in a flat Friedmann universe. Providing the back reaction of the scalar field on the metric can be neglected, we find that the value of the scalar field at the event horizon very quickly assumes the background cosmological value. This suggests that there is very little gravitational memory.

The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As shown previously, for a neutral nonrotating black hole, such eigenvalues must be $2^n$-fold degenerate if one constructs the black hole stationary states by means of a pair of creation operators subject to a specific algebra. We show that the algebra of these two building blocks exhibits $U\left(2\right)\mathrm{}\equiv U\left(1\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$ symmetry, where the area operator generates the $U\left(1\right)\mathrm{}$ symmetry. The three generators of the $\mathrm{SU}\left(2\right)\mathrm{}$ symmetry represent a global quantum number (hyperspin) of the black hole, and we show that this hyperspin must be zero. As a result, the degeneracy of the n-th area eigenvalue is reduced to $2^n{/n}^{3/2}$ for large n, and therefore, the logarithmic correction term $-3/2\log A$ should be added to the Bekenstein-Hawking entropy. We also provide a heuristic approach explaining this result, and evidence for the existence of two building blocks.

We numerically reanalyze static and spherically symmetric black hole solutions in an Einstein-Maxwell-dilaton system with a dilaton potential $m_d^2{\phi }^2.$ We investigate thermodynamic properties for various dilaton coupling constants and find that thermodynamic properties change at a critical dilaton mass $m_{d,\mathrm{crit}}.$ For $m_d>~m_{d,\mathrm{crit}},$ the black hole becomes an extreme solution for a nonzero horizon radius $r_{h,\mathrm{ex}}$ as the Reissner-Nordström black hole does. However, if $m_d$ is nearly equal to $m_{d,\mathrm{crit}},$ there appears a solution of smaller horizon radius than $r_{h,\mathrm{ex}}.$ For $m_d<m_{d,\mathrm{crit}},$ a solution continues to exist until the horizon approaches zero. The Hawking temperature in the zero horizon limit resembles that of a massless dilaton black hole for an arbitrary dilaton coupling constant.

When a potential for a scalar field has two local minima there arise spherical shell-type solutions of the classical field equations due to gravitational attraction. We establish such solutions numerically in a space which is asymptotically de Sitter. It generically arises when the energy scale characterizing the scalar field potential is much less than the Planck scale. It is shown that the mirror image of the shell appears in the other half of the Penrose diagram. The configuration is smooth everywhere with no physical singularity.

We present the first computations of quasiequilibrium binary neutron stars with different mass components in general relativity, within the Isenberg-Wilson-Mathews approximation. We consider both cases of synchronized rotation and irrotational motion. A polytropic equation of state is used with the adiabatic index $\gamma =2.\mathrm{}$ The computations have been performed for the following combinations of stars: ${\mathrm{}(M/R)\mathrm{}}_{\infty ,\mathrm{star}1}$ vs ${\mathrm{}(M/R)\mathrm{}}_{\infty ,\mathrm{star}2}=0.12\mathrm{}\mathrm{vs}\mathrm{}(0.12,0.13,0.14),$ $0.14\mathrm{vs}\mathrm{}(0.14,0.15,0.16),$ $0.16\mathrm{vs}\mathrm{}(0.16,0.17,0.18),$ $\mathrm{and}0.18\mathrm{vs}0.18,$ where ${\mathrm{}(M/R)\mathrm{}}_{\infty }$ denotes the compactness parameter of infinitely separated stars of the same baryon number. It is found that for identical mass binary systems there is no turning point of the binding energy (ADM mass) before the end point of the sequence (mass shedding point) in the irrotational case, while there is one before the end point of the sequence (contact point) in the synchronized case. On the other hand, in the different mass case, the sequence ends by the tidal disruption of the less massive star (mass shedding point). It is then more difficult to find a turning point in the ADM mass. Furthermore, we find that the deformation of each star depends mainly on the orbital separation and the mass ratio and very weakly on its compactness. On the other side, the decrease of the central energy density depends on the compactness of the star and not on that of the companion.

We analyze the spectrum of perturbations of de Sitter space on the one hand, while on the other hand we compute the location of the poles in the conformal field theory (CFT) propagator at the border. The coincidence is striking, supporting a dS/CFT correspondence. We show that the spectrum of thermal excitations of the CFT at the past boundary $I^{-}$ together with that spectrum at the future boundary $I^{+}$ is contained in the quasinormal mode spectrum of the de Sitter space in the bulk.

We extend existing work on the propagation of ultrahigh energy cosmic rays in extragalactic magnetic fields to a possible component of heavy nuclei, taking into account photodisintegration, pion production, and the creation of $e^{\pm }$ pairs. We focus on the influence of the magnetic field on the spectrum and chemical composition of observed ultrahigh energy cosmic rays. We apply our simulations to the scenarios proposed by Anchordoqui et al., in which iron nuclei are accelerated in nearby starburst galaxies, and show that it is in marginal agreement with the data. We also show that it is highly unlikely to detect He nuclei from M87 at the highest energies observed $\sim 3\times {10}^{20}\mathrm{eV}$ as required for the scenario of Ahn et al. in which the highest energy cosmic rays originate from M87 and are deflected in a Parker spiral galactic magnetic field.

We introduce a method to obtain deformed defects starting from a given scalar field theory which possesses defect solutions. The procedure allows the construction of infinitely many new theories that support defect solutions, analytically expressed in terms of the defects of the original theory. The method is general, valid for both topological and nontopological defects, and we show how it extends to quantum mechanics and how it works when the scalar field couples to fermions. We illustrate the general procedure with several examples, which support kinklike or lumplike defects.

We present a classification of the unitarity quadrangles in the four-neutrino mixing scheme. We find that there are totally thirty-six distinct topologies among twelve different unitarity quadrangles. Concise relations are established between the areas of those unitarity quadrangles and the rephasing invariants of $\mathrm{CP}$ and T violation.

The thermal properties of glueballs are studied using SU(3) anisotropic lattice QCD with ${\beta }_{\mathrm{lat}}=6.25,$ the renormalized anisotropy $\xi \equiv a_s{/a}_t=4\mathrm{}$ over the lattice of the size ${20}^3\times N_t$ with $N_t=24,$ 26, 28, 30, 33, 34, 35, 36, 37, 38, 40, 43, 45, 50, 72 at the quenched level. To construct a suitable operator for the lowest-state glueball on the lattice, we adopt the smearing method, providing an illustration of its physical meaning in terms of the operator size. First, we construct the temporal correlators $G\left(t\right)\mathrm{}$ for the lowest $0^{++}$ and $2^{++}$ glueballs, using more than 5500 gauge configurations at each temperature $T.\mathrm{}$ We then perform the pole-mass measurement of the thermal glueballs from $G\left(t\right).$ For the lowest $0^{++}$ glueball, we observe a significant pole-mass reduction of about 300 MeV in the vicinity of $T_c$ or $m_G\left(T\simeq T_c\right)\simeq {0.8m}_G\left(T\sim 0\right),$ while its size remains almost unchanged as $\rho \mathrm{}\left(T\right)\mathrm{}\simeq 0.4\mathrm{fm}.$ Finally, for completeness, as an attempt to take into account the effect of the thermal width $\Gamma \mathrm{}\left(T\right)\mathrm{}$ at finite temperature, we perform a more general new analysis of $G\left(t\right)\mathrm{}$ based on its spectral representation. As an ansatz to the spectral function $\rho \left(\omega \right),$ we adopt the Breit-Wigner form, and perform the best-fit analysis of the temporal correlator as a straightforward extension to the standard pole-mass analysis. The result indicates a significant broadening of the peak as $\Gamma \mathrm{}\left(T\right)\mathrm{}\sim 300\mathrm{MeV}$ as well as a rather modest reduction of the peak center of about 100 MeV near $T_c$ for the lowest $0^{++}$ glueball. The temporal correlators of the color-singlet modes corresponding to these glueballs above $T_c$ are also investigated.

In this third part of our calculation of the QCD next-to-leading order corrections to the photon impact factor we combine our previous results for the real corrections with the singular pieces of the virtual corrections and present finite analytic expressions for the quark-antiquark-gluon intermediate state inside the photon impact factor. We begin with a list of the infrared singular pieces of the virtual correction, obtained in the first step of our program. We then list the complete results for the real corrections (longitudinal and transverse photon polarization). In the next step we define, for the real corrections, the collinear and soft singular regions and calculate their contributions to the impact factor. We then subtract the contribution due to the central region. Finally, we combine the real corrections with the singular pieces of the virtual corrections and obtain our finite results.

We compute the pion light-cone wave function and the pion quark distribution amplitude in the Nambu–Jona-Lasinio model. We use the Pauli-Villars regularization method and as a result the distribution amplitude satisfies proper normalization and crossing properties. In the chiral limit we obtain the simple results, namely ${\phi }_{\pi }\mathrm{}\left(x\right)=1\mathrm{}$ for the pion distribution amplitude, and $\int d^2{k}_{\perp }{\Psi }_{\pi }(x,k_{\perp }{)k}_{\perp }^2=〈k_{\perp }^2〉=-M〈ūu〉{/f}_{\pi }^2$ for the second moment of the pion light-cone wave function, where M is the constituent quark mass and $f_{\pi }$ is the pion decay constant. After the QCD Gegenbauer evolution of the pion distribution amplitude good end-point behavior is recovered, and a satisfactory agreement with the analysis of the experimental data from CLEO is achieved. This allows us to determine the momentum scale corresponding to our model calculation, which is close to the value $Q_0=313\mathrm{}\mathrm{MeV}$ obtained earlier from the analogous analysis of the pion parton distribution function. The value of $〈k_{\perp }^2〉$ is, after the QCD evolution, around $(400\mathrm{}\mathrm{MeV}{)}^2.$ In addition, the model predicts a linear integral relation between the pion distribution amplitude and the parton distribution function of the pion, which holds at the leading-order QCD evolution.

We report the results of a study of two-body B meson decays to the complete set of $K\pi ,$ $\pi \pi ,$ and $K\overline{K}$ final states. The study is performed on a data sample of $31.7\pm 0.3$ million $B\overline{B}$ events recorded on the ${\rm Y}\left(4\mathrm{}\mathrm{S}\right)$ resonance by the Belle experiment at KEKB. We observe significant signals in all $K\pi$ final states and in the ${\pi }^{+}{\pi }^{-}$ and ${\pi }^{+}{\pi }^0$ final states. We set limits on the ${\pi }^0{\pi }^0$ and $K\overline{K}$ final states. A search is performed for partial-rate asymmetries between conjugate states for flavor-specific final states.

Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of type-IIB string theory and F-theory compactifications on Calabi-Yau fourfolds. In each case, the hierarchy of scales is fixed by a choice of Ramond-Ramond and Neveu-Schwarz fluxes in the compact manifold. Our solutions involve compactifications of the Klebanov-Strassler gravity dual to a confining $\mathcal{N}=1\mathrm{}$ supersymmetric gauge theory, and the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory.

A class of exact solutions of the Skyrme and the Faddeev models is presented. In contrast with previously found solutions, they are produced by the interplay of the two terms in the Lagrangians of the models. They are not solitonic but are of wave character. With an appropriate choice of field variables, the field equations of the two models are written in exactly the same form. The solutions supply us with examples of the superposition of two plane waves in nonlinear field theories.

We study the quantum-mechanical consistency of noncommutative gauge theories by perturbatively analyzing the Wilsonian quantum effective action in the matrix formulation. In the process of integrating out UV states, we find new divergences having dual UV-IR interpretations and no analogues in ordinary quantum field theories. The appearance of these new UV-IR divergences has profound consequences for the renormalizability of the theory. In particular, renormalizability fails in any nonsupersymmetric noncommutative gauge theory. In fact, we argue that renormalizability generally fails in any noncommutative theory that allows quantum corrections beyond one loop. Thus, it seems that noncommutative quantum theories are extremely sensitive to the UV, and only the softest UV behavior can be tolerated.

Classical noncommutative (NC) Q-ball solutions are shown to analytically reduce to their commutative analogue. Then such a NC Q ball is canonically quantized and the quantum correction to its energy is calculated through the summation of the phase shift. The same method is generalized to the NC Gopakumar-Minwalla-Strominger (GMS) soliton for a smooth enough solution. In both cases UV-IR mixing is found in the energy corrections. UV divergence is shown to be absent for a NC GMS soliton. We conclude by discussing the physical implications of UV-IR terms in the energy of NC solitons.