The rare decay $B^0\to \gamma \gamma$ is searched for in $104{\mathrm{fb}}^{-1}$ of data, corresponding to $111\times {10}^{6}B\overline{B}$ pairs, collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. No evidence for the signal is found, and an upper limit of $6.2\times {10}^{-7}$ at 90% confidence level is set for the corresponding branching fraction.

The spontaneous breakdown of 4-dimensional Lorentz invariance in the framework of QED with the nonlinear vector potential constraint $A_{\mu }^2=M^2$ (where $M$ is a proposed scale of the Lorentz violation) is shown to manifest itself only as some noncovariant gauge choice in the otherwise gauge invariant (and Lorentz invariant) electromagnetic theory. All the contributions to the photon-photon, photon-fermion, and fermion-fermion interactions violating the physical Lorentz invariance happen to be exactly cancelled with each other in the manner observed by Nambu long ago for the simplest tree-order diagrams—the fact which we extend now to the one-loop approximation and for both the timelike ($M^2>0$) and spacelike ($M^2<0$) Lorentz violations. The way to reach the physical breaking of the Lorentz invariance in the pure QED case (and beyond) treated in the flat Minkowskian space-time is also discussed in some detail.

Inflation in a five-dimensional brane world model with two boundary branes is studied. We make use of the moduli space approximation whereby the low energy theory reduces to a four-dimensional biscalar-tensor gravity plus a minimally coupled scalar field. After a detailed analysis of the inflationary solutions, we derive the evolution equations of the linear perturbations separating the adiabatic mode from two entropy modes. We then examine the primordial scalar and tensor power spectra and show that their tilt depends on the scalar-tensor coupling constant. Finally, the induced cosmic microwave background (CMB) anisotropies are computed and we present a Monte Carlo Markov chains exploration of the parameter space using the first year WMAP data. We find a marginalized probability bound for the associated Eddington parameter at the end of inflation $1-\gamma <2\times {10}^{-3}$, at 95% confidence level. This suggests that future CMB data could provide crucial information helping to distinguish scalar-tensor and standard inflationary scenarios.

We study in detail the quasinormal modes of linear gravitational perturbations of plane-symmetric anti-de Sitter black holes. The wave equations are obtained by means of the Newman-Penrose formalism and the Chandrasekhar transformation theory. We show that oscillatory modes decay exponentially with time such that these black holes are stable against gravitational perturbations. Our numerical results show that in the large (small) black hole regime the frequencies of the ordinary quasinormal modes are proportional to the horizon radius $r_{+}$ (wave number $k$). The frequency of the purely damped mode is very close to the algebraically special frequency in the small horizon limit, and goes as $i{k}^2/3r_{+}$ in the opposite limit. This result is confirmed by an analytical method based on the power series expansion of the frequency in terms of the horizon radius. The same procedure applied to the Schwarzschild anti-de Sitter spacetime proves that the purely damped frequency goes as $i(l-1)(l+2)/3r_{+}$, where $l$ is the quantum number characterizing the angular distribution. Finally, we study the limit of high overtones and find that the frequencies become evenly spaced in this regime. The spacing of the frequency per unit horizon radius seems to be a universal quantity, in the sense that it is independent of the wave number, perturbation parity, and black hole size.

We discuss constraints on which flat directions can have large vacuum expectation values (VEVs) after inflation. We show that only flat directions which are not charged under $\mathrm{B}-\mathrm{L}$ and develop positive pressure due to renormalization group effects can have large VEVs of order $M_{\mathrm{Pl}}$. For example, within the MSSM only the $H_u{H}_d$ flat direction is found to be viable. This strongly constrains the embedding of a broad class of inflationary models in the MSSM or some other supersymmetric extension of the SM. For flat directions with negative pressure, the condensate fragments into very large Q-balls which we call Q-giants. We discuss the formation, evolution and reheating of these Q-giants and show that they decay too late. The analysis requires taking into account new phases of the flat directions, which have been overlooked in the formation and dynamics of the Q-balls. These constraints may be ameliorated by invoking a short period of thermal inflation. The latter, however, is viable in a very narrow window of parameter space and requires fine tuning.

We study the conditions of validity of the generalized second law in phantom-dominated era.

This work presents the first application of the method of genetic algorithms (GAs) to data analysis for the Laser Interferometer Space Antenna (LISA). In the low frequency regime of the LISA band there are expected to be tens of thousands of galactic binary systems that will be emitting gravitational waves detectable by LISA. The challenge of parameter extraction of such a large number of sources in the LISA data stream requires a search method that can efficiently explore the large parameter spaces involved. As signals of many of these sources will overlap, a global search method is desired. GAs represent such a global search method for parameter extraction of multiple overlapping sources in the LISA data stream. We find that GAs are able to correctly extract source parameters for overlapping sources. Several optimizations of a basic GA are presented with results derived from applications of the GA searches to simulated LISA data.

We construct a version of the top mode standard model where the third generation fermions and the $SU(2{)}_L\times U(1{)}_Y$ gauge bosons are put on a 6-dimensional brane (5-brane) with the extra dimensions compactified on the TeV scale ($R_5^{-1}=R_6^{-1}\equiv R^{-1}=1\mathrm{\text{−}}10\mathrm{TeV}$), while only the gluons live in a compactified 8-dimensional bulk ($R_7^{-1}=R_8^{-1}\equiv \Lambda \gg R^{-1}$). On the 5-brane, Kaluza-Klein (KK) modes of the bulk gluons give rise to induced four-fermion interactions which, combined with the gauge interactions, are shown to be strong enough to trigger the top quark condensate, based on the dynamics of 6-dimensional gauged Nambu-Jona-Lasinio (NJL) model. Moreover, we can use a freedom of the brane positions to tune the four-fermion coupling close to the critical line of 6-dimensional gauged NJL model, so that the gap equation can ensure the top condensate on the weak scale while keeping other fermions massless. There actually exists a scale (“tMAC scale”), ${\Lambda }_{\mathrm{tM}}=(7.8\mathrm{\text{−}}11.0)R^{-1}$, where the running gauge couplings combined with the induced four-fermion interactions trigger only the top condensate while no bottom and tau condensates. Furthermore, presence of such explicit four-fermion interactions enables us to formulate straightforwardly the compositeness conditions at $\Lambda ={\Lambda }_{\mathrm{tM}}$, which, through the renormalization-group analysis, yields a prediction of masses of the top quark and the Higgs boson, $m_t=177\mathrm{\text{−}}187\mathrm{GeV}$ and $m_H=183\mathrm{\text{−}}207\mathrm{GeV}$.

We study exclusive nonleptonic and semileptonic decays of the $B_c$-meson within a relativistic constituent quark model previously developed by us. For the nonleptonic decays we use the factorizing approximation. We update our model parameters by using new experimental data for the mass and the lifetime of the $B_c$ meson and the leptonic decay constants of the $D$-meson. We calculate the branching ratios for a large set of exclusive nonleptonic and semileptonic decays of the $B_c$ meson and compare our results with the results of other studies. As a guide for further experimental exploration we provide explicit formulas for the full angular decay distributions in the cascade decays $B_c^{-}\to J/\psi (\to l^{+}{l}^{-})+{\rho }^{-}(\to {\pi }^{-}{\pi }^0)$ and $B_c^{-}\to J/\psi (\to l^{+}{l}^{-})+W_{\mathrm{off}\mathrm{\text{−}}\mathrm{shell}}^{-}(\to l^{-}+{\overline{\nu }}_l)$.

We present the results of calculations analyzing nucleon Compton scattering to lowest order using perturbative QCD (pQCD) methods. Two scenarios are considered: (1) the incoming photon is real; and (2) the incoming photon is virtual. The case of a real photon has been previously analyzed at least 5 times using pQCD, but no two results are in agreement. Here it is shown that our result agrees with that of Brooks and Dixon published in 2000. The case of a virtual photon has been previously analyzed only once using pQCD. However, doubt has been cast on the validity of that result. The results presented here for the virtual photon are believed to be more reliable. Some consideration is given of how to compare these results with experiment. Following the lead of Brooks and Dixon, for the proton, this involves normalizing the cross section using the Dirac proton form factor, which we also calculate. Finally, there is a comparison of our results with recent experiments.

It is well known that high energy data alone do not discriminate between asymptotic $\ln s$ and ${ln}^{2}s$ behavior of $pp$ and $\overline{p}p$ cross sections. By exploiting high quality low energy data, analyticity resolves this ambiguity in favor of cross sections that grow asymptotically as ${ln}^{2}s$. We here show that two methods for incorporating the low energy data into the high energy fits give numerically identical results and yield essentially identical tightly constrained values for the LHC cross section. The agreement can be understood as a new analyticity constraint derived as an extension of a finite energy sum rule.

We show that there exist a large class of new nontrivial exactly solvable models with their potentials depending only on one spatial variable on a 2D noncommutative plane and show that their general solutions are Schrödinger cat states. This feature not only establishes an interesting connection between quantum mechanics on noncommutative spaces and quantum information science but also shed light on proposing new schemes based on the quantum entanglement to test the noncommutativity.

At the core of nonperturbative theories of quantum gravity lies the holographic encoding of bulk data in large matrices. At present this mapping is poorly understood. The plane wave matrix model provides a laboratory for isolating aspects of this problem in a controlled setting. At large boosts, configurations of concentric membranes become superselection sectors, whose exact spectra are known. From the bulk point of view, one expects product states of individual membranes to be contained within the full spectrum. However, for non-BPS states this inclusion relation is obscured by Gauss law constraints. Its validity rests on nontrivial relations in representation theory, which we identify and verify by explicit computation.

We compute the strong coupling limit of the shear viscosity for the $\mathcal{N}=4$ super-Yang-Mill theory with a chemical potential. We use the five-dimensional Reissner-Nordström-anti-deSitter black hole, so the chemical potential is the one for the $R$-charges $U(1{)}_R^3$. We compute the quasinormal frequencies of the gravitational and electromagnetic vector perturbations in the background numerically. This enables one to explicitly locate the diffusion pole for the shear viscosity. The ratio of the shear viscosity $\eta$ to the entropy density $s$ is $\eta /s=1/(4\pi )$ within numerical errors, which is the same result as the one without chemical potential.

We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree-level approximation. In the one-loop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the brane—the inverse of the brane-to-brane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent well-known difficulties in the heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowest-order surface terms in the case of Robin and oblique boundary onditions. We briefly discuss multiloop applications of the suggested Dirichlet reduction and the prospects of constructing the universal background-field method for systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.

We discuss the options for parity assignments in (on-shell) $\mathcal{N}=2$ five-dimensional Yang-Mills-Einstein supergravity theories (YMESGTs) coupled to tensor and hypermultiplets on the orbifold spacetime ${\mathcal{M}}_4\times S^1/{\mathbb{Z}}_2$. Along the lines of orbifold-grand unified theories (GUTs), we allow for general breaking of the five-dimensional gauge group at the orbifold fixed points. We then extend the discussion to the case where the orbifold is $S^1/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$. We do not presume the existence of fields with support only at fixed points. As in the familiar case of (rigid) super-Yang-Mills theories on such orbifolds, only bulk hypermultiplets can lead to chiral multiplets in complex representations of the gauge group on the boundaries. Massless chiral multiplets coming from bulk vector or tensor multiplets can potentially be used as Higgs supermultiplets, though a “doublet-triplet” splitting via parity assignments is not available for the tensor sector. We also find parity assignments for objects other than fields that appear in the Lagrangian, which will partially determine the structure of interactions of the boundary theories. Assigning odd parities to the scalar sector of vector/tensor multiplets requires the four-dimensional boundary moduli spaces to lie on the boundary of the classical Kähler cone, which corresponds to collapsed Calabi-Yau 2-cycles at the orbifold fixed points in a compactification of 11-dimensional supergravity. There is an ambiguity in how to affect odd parity for the field-independent $C_{IJK}$ tensor of the 5D theory, which may admit a classical interpretation as Calabi-Yau 4-cycles collapsing to either 2- or 0-cycles.

We elucidate the geometry of the polynomial formulation of the non-Abelian Stueckelberg mechanism. We show that a natural off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) differential exists allowing to implement the constraint on the $\sigma$ field by means of BRST techniques. This is achieved by extending the ghost sector by an additional U(1) factor (Abelian embedding). An important consequence is that a further BRST-invariant but not gauge-invariant mass term can be written for the non-Abelian gauge fields. As all versions of the Stueckelberg theory, also the Abelian embedding formulation yields a nonpower-counting renormalizable theory in $D=4$. We then derive its natural power-counting renormalizable extension and show that the physical spectrum contains a physical massive scalar particle. Physical unitarity is also established. This model implements the spontaneous symmetry breaking in the Abelian embedding formalism.

In the presence of a strong magnetic field, the effective action of a composite scalar field in a scalar $O(N)$ model is derived using two different methods. First, in the framework of world-line formalism, the 1PI $n$-point vertex function for the composites is determined in the limit of a strong magnetic field. Then, the $n$-point effective action of the composites is calculated in the regime of lowest Landau level dominance. It is shown that in the limit of a strong magnetic field, the results coincide and an effective field theory arises which is comparable with the conventional noncommutative field theory. In contrast to the ordinary case, however, the UV/IR mixing is absent in this modified noncommutative field theory.

Twistors in four dimensions $d=4$ have provided a convenient description of massless particles with any spin, and this led to remarkable computational techniques in Yang-Mills field theory. Recently it was shown that the same $d=4$ twistor provides also a unified description of an assortment of other particle dynamical systems, including special examples of massless or massive particles, relativistic or nonrelativistic, interacting or noninteracting, in flat space or curved spaces. In this paper, using 2T-physics as the primary theory, we derive the general twistor transform in $d$-dimensions that applies to all cases, and show that these more general twistor transforms provide $d$ dimensional holographic images of an underlying phase space in flat spacetime in $d+2$ dimensions. Certain parameters, such as mass, parameters of spacetime metric, and some coupling constants, appear as moduli in the holographic image while projecting from $d+2$ dimensions to $(d-1)+1$ dimensions or to twistors. We also extend the concept of twistors to include the phase space of D-branes, and give the corresponding twistor transform. The unifying role for the same twistor that describes an assortment of dynamical systems persists in general, including D-branes. Except for a few special cases in low dimensions that exist in the literature, our twistors are new.