We consider ($3+1$)-dimensional $\mathcal{N}=2$ supersymmetric QED with two flavors of fundamental hypermultiplets. This theory supports $1/2$-Bogomol’nyi-Prasad-Sommerfield (BPS) domain walls and flux tubes (strings), as well as their $1/4$-BPS junctions. The effective ($2+1$)-dimensional theory on the domain wall is known to be a U(1) gauge theory. Previously, the wall-string junctions were shown to play the role of massive charges in this theory. However, the field theory of the junctions on the wall (for semi-infinite strings) appears to be inconsistent due to infrared problems. All these problems can be eliminated by compactifying one spatial dimension orthogonal to the wall and considering a wall-antiwall system ($W\overline{W}$) on a cylinder. We argue that for certain values of parameters this setup provides a controllable analog of bulk-brane duality in field theory. Dynamics of the 4D bulk are mapped onto 3D boundary theory: 3D $\mathcal{N}=2$ supersymmetric quantum electrodynamics (SQED) with two matter superfields and a weak-strong coupling constant relation in 4D and 3D, respectively. The cylinder radius is seen as a “real mass” in 3D $\mathcal{N}=2$ SQED. We work out (at weak coupling) the quantum version of the world-volume theory on the walls. Integrating out massive matter (strings in the bulk theory) one generates a Chern-Simons term on the wall world volume and an interaction between the wall and antiwall that scales as a power of distance. Vector and scalar (classically) massless excitations on the walls develop a mass gap at the quantum level; the long-range interactions disappear. The above duality implies that the wall and its antiwall partner (at strong coupling in the bulk theory) are stabilized at the opposite sides of the cylinder.

It is now established that small Kerr–anti-de Sitter (Kerr-AdS) black holes are unstable against scalar perturbations, via the superradiant amplification mechanism. We show that small Kerr-AdS black holes are also unstable against gravitational perturbations and we compute the features of this instability. We also describe with great detail the evolution of this instability. In particular, we identify its end-point state. It corresponds to a Kerr-AdS black hole whose boundary is an Einstein universe rotating with the light velocity. This black hole is expected to be slightly oblate and to coexist in equilibrium with a certain amount of outside radiation.

We examine the Euclidean action approach, as well as that of Wald, to the entropy of black holes in asymptotically AdS spaces. From the point of view of holography these two approaches are somewhat complementary in spirit and it is not obvious why they should give the same answer in the presence of arbitrary higher derivative gravity corrections. For the case of the ${\mathrm{AdS}}_5$ Schwarzschild black hole, we explicitly study the leading correction to the Bekenstein-Hawking entropy in the presence of a variety of higher derivative corrections studied in the literature, including the Type IIB $R^4$ term. We find a nontrivial agreement between the two approaches in every case. Finally, we give a general way of understanding the equivalence of these two approaches.

We propose a toy model for studying merger transitions in a curved spacetime with an arbitrary number of dimensions. This model includes a bulk $N$-dimensional static spherically symmetric black hole and a test $D$-dimensional brane ($D\le N-1$) interacting with the black hole. The brane is asymptotically flat and allows a $O(D-1)$ group of symmetry. Such a brane–black-hole (BBH) system has two different phases. The first one is formed by solutions describing a brane crossing the horizon of the bulk black hole. In this case the internal induced geometry of the brane describes a $D$-dimensional black hole. The other phase consists of solutions for branes which do not intersect the horizon, and the induced geometry does not have a horizon. We study a critical solution at the threshold of the brane–black-hole formation, and the solutions which are close to it. In particular, we demonstrate that there exists a striking similarity of the merger transition, during which the phase of the BBH system is changed, both with the Choptuik critical collapse and with the merger transitions in the higher dimensional caged black-hole–black-string system.

Nonperturbative quantum geometric effects in loop quantum cosmology (LQC) predict a ${\rho }^2$ modification to the Friedmann equation at high energies. The quadratic term is negative definite and can lead to generic bounces when the matter energy density becomes equal to a critical value of the order of the Planck density. The nonsingular bounce is achieved for arbitrary matter without violation of positive energy conditions. By performing a qualitative analysis we explore the nature of the bounce for inflationary and cyclic model potentials. For the former we show that inflationary trajectories are attractors of the dynamics after the bounce implying that inflation can be harmoniously embedded in LQC. For the latter difficulties associated with singularities in cyclic models can be overcome. We show that nonsingular cyclic models can be constructed with a small variation in the original cyclic model potential by making it slightly positive in the regime where scalar field is negative.

The possibility that the Universe may have a fundamental and positive cosmological constant has motivated an interesting cosmological model, in which initially the Universe is in a cosmological constant sea, then the local quantum fluctuations violating the null energy condition create some islands with matter and radiation, which under certain conditions might correspond to our observable universe. We in this paper study the perturbation spectra of scalar fields not affecting the evolution of background during the fluctuation. We will examine whether they can be interesting, and responsible for the structure formation of the observable universe.

Inflation with tunneling from a false to a true vacuum becomes viable in the presence of a scalar field that slows down the initial de Sitter phase. As a by-product this field also sets dynamically the value of $M_{\mathrm{Planck}}$ observed today. This can be very large if the tunneling rate (which is exponentially sensitive to the barrier) is small enough. Therefore along with inflation we also provide a natural dynamical explanation for why gravity is so weak today. Moreover we predict a spectrum of gravity waves peaked at around 0.1 mHz, that will be detectable by the planned space interferometer LISA. Finally we discuss interesting predictions on cosmological scalar and tensor fluctuations in light of the WMAP 3-year data.

We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect.

We investigated two pion condensed phases in the frame of the two flavor Nambu-Jona-Lasinio model at finite baryon density: the homogeneous and isotropic Sarma phase and inhomogeneous and anisotropic Larkin-Ovchinnikov-Fudde-Ferrell (LOFF) phase. At small isospin chemical potential ${\mu }_I$, the Sarma state is free from the Sarma instability and magnetic instability due to the strong coupling and large enough effective quark mass. At large ${\mu }_I$, while the Sarma instability can be cured via fixing baryon density $n_B$ to be nonzero, its magnetic instability implies that the LOFF state is more favored than the Sarma state. In the intermediate ${\mu }_I$ region, the stable ground state is the Sarma state at higher $n_B$ and the LOFF state at lower $n_B$.

It is shown that in the 70 and 700 SU(6) irreducible spaces, the SU(6) extension of the Weinberg-Tomozawa (WT) $s$-wave meson-baryon interaction incorporating vector mesons (hep-ph/0505233) scales as $\mathcal{O}(N_c^0)$, instead of the well-known $\mathcal{O}(N_c^{-1})$ behavior for its SU(3) counterpart. However, the WT interaction behaves as order $\mathcal{O}(N_c^{-1})$ within the 56 and 1134 meson-baryon spaces. Explicit expressions for the WT couplings (eigenvalues) in the irreducible $\mathrm{SU}(2N_F)$ spaces, for arbitrary $N_F$ and $N_c$, are given. This extended interaction is used as a kernel of the Bethe Salpeter equation, to study the large $N_c$ scaling of masses and widths of the lowest-lying negative parity $s$-wave baryon resonances. Analytical expressions are found in the $N_c\to \infty$ limit, from which it can be deduced that resonance widths and excitation energies ($M_R-M$) behave as order $\mathcal{O}(N_c^0)$, in agreement with model independent arguments, and moreover they fall in the 70-plet, as expected in constituent quark models for an orbital excitation. For the 56 and 1134 spaces, excitation energies and widths grow $\mathcal{O}(N_c^{1/2})$ indicating that such resonances do not survive in the large $N_c$ limit. The relation of this latter $N_c$ behavior with the existence of exotic components in these resonances is discussed. The interaction comes out repulsive in the 700.

Conditions for $CP$ violation in the scalar potential sector of general $N$-Higgs-doublet models are analyzed from a group theoretical perspective. For the simplest two-Higgs-doublet model potential, a minimum set of conditions for explicit and spontaneous $CP$ violation is presented. The conditions can be given a clear geometrical interpretation in terms of quantities in the adjoint representation of the basis transformation group for the two doublets. Such conditions depend on $CP$-odd pseudoscalar invariants. When the potential is $CP$ invariant, the explicit procedure to reach the real $CP$-basis and the explicit $CP$ transformation can also be obtained. The procedure to find the real basis and the conditions for $CP$ violation are then extended to general $N$-Higgs-doublet model potentials. The analysis becomes more involved and only a formal procedure to reach the real basis is found. Necessary conditions for $CP$ invariance can still be formulated in terms of group invariants: the $CP$-odd generalized pseudoscalars. The problem can be completely solved for three Higgs-doublets.

We have performed numerical simulations of the unpolarized $e^{+}{e}^{-}\to p\overline{p}$ process in kinematic conditions under discussion for a possible upgrade of the existing DAFNE facility. By fitting the cross section angular distribution with a typical Born expression, we can extract information on the ratio $|G_E/G_M|$ of the proton electromagnetic form factors in the timelike region within a 5%–10% uncertainty. We have explored also non-Born contributions to the cross section by introducing a further component in the angular fit, which is related to two-photon exchange diagrams. We show that these corrections can be identified if larger than 5% of the Born contribution, and if relative phases of the complex form factors do not produce severe cancellations.

We analyze the $\pi {\gamma }^{*}{\gamma }^{*}$ amplitude in the framework of radial Regge models in the large-$N_c$ limit. With the assumption of similarity of the asymptotic Regge $\rho$ and $\omega$ meson spectra we find that the pion distribution amplitude is constant in the large-$N_c$ limit at the scale $Q_0$ where the QCD radiative corrections are absent—a result found earlier in a class of chiral quark models. We discuss the constraints on the couplings from the anomaly and from the limit of large photon virtualities, and find that the coupling of the pion to excited $\rho$ and $\omega$ mesons must be asymptotically constant. We also discuss the effects of the QCD evolution on the pion electromagnetic transition form factor. Finally, we use the Regge model to evaluate the slope of the form factor at zero momentum and compare the value to the experiment, finding very reasonable agreement.

We investigate characteristics of the signal and backgrounds for Higgs boson decay into $WW$ at the Fermilab Tevatron and CERN Large Hadron Collider. In the lepton-pair-plus-missing-energy final state, we show that the background receives an important contribution from semileptonic decays of heavy flavors. Lepton isolation cuts provide too little suppression of these heavy flavor contributions, and an additional 4 to 8 orders-of-magnitude suppression must come from physics cuts. We demonstrate that an increase of the minimum transverse momentum of nonleading leptons in multilepton events is one effective way to achieve the needed suppression, without appreciable loss of the Higgs boson signal. Such a cut would impact the efficiency of searches for supersymmetry as well. We emphasize the importance of direct measurement of the lepton background from heavy flavor production.

We use the method of QCD sum rules to investigate the isospin symmetry breaking of $K$ and $K^{*}$ mesons. The electromagnetic effect, difference between up and down current-quark masses and difference between up and down quark condensates are important. We perform sum rule analyses of their masses and decay constant differences, which are consistent with experimental values. Our results yield $\Delta f_K=f_{K^0}-f_{K^{\pm }}=1.5\mathrm{MeV}$.

We study the zero-dimensional reduced model of $D=6$ pure super Yang-Mills theory and argue that the large $N$ limit describes the (2,0) Little String Theory. The one-loop effective action shows that the force exerted between two diagonal blocks of matrices behaves as $1/r^4$, implying a six-dimensional spacetime. We also observe that it is due to nongravitational interactions. We construct wave functions and vertex operators which realize the $D=6$, (2,0) tensor representation. We also comment on other little analogues of the IIB matrix model and Matrix Theory with less supercharges.

Conformal symmetry is a powerful tool used to study field theories at their critical points. The enlargement of the space-time symmetry allows to classify local operators according to their conformal dimension. We propose a similar classification of nonlocal objects, like defects, vortices or Wilson loops, which may exist in conformal field theories. The definition relies on representations of subgroups of the conformal group and this new notion analogous to the conformal dimension may have wide applications in a variety of conformal field theories. We demonstrate the uses of this method to the study of Wilson loops in a conformal gauge theory.

We construct a new off-shell $\mathcal{N}=8$, $d=1$ nonlinear supermultiplet $(\mathbf{4},\mathbf{8},\mathbf{4})$ proceeding from the nonlinear realization of the $\mathcal{N}=8$, $d=1$ superconformal group $OSp(4^{\star }|4)$ in its supercoset $\frac{OSp(4^{\star }|4)}{SU(2{)}_{\mathcal{R}}\otimes \{D,K\}\otimes SO(4)}$. The irreducibility constraints for the superfields automatically follow from appropriate covariant conditions on the $osp(4^{\star }|4)$-valued Cartan superforms. We present the most general sigma-model type action for $(\mathbf{4},\mathbf{8},\mathbf{4})$ supermultiplet. The relations between linear and nonlinear $(\mathbf{4},\mathbf{8},\mathbf{4})$ supermultiplets and linear $\mathcal{N}=8$ $(\mathbf{5},\mathbf{8},\mathbf{3})$ vector supermultiplet are discussed.

The ultraviolet regularization of Yukawa theory in de Sitter space is considered. We rederive the one-loop effective Candelas-Raine potentials, such that they agree with the corresponding Coleman-Weinberg potentials in flat space. Within supersymmetry, this provides a mechanism for the lifting of flat directions during inflation. For the purpose of calculating loop integrals, we employ the dimensional regularization procedure by Onemli and Woodard and show explicitly that the resulting self-energies are also invariant. This implies the absence of anomalous de Sitter breaking terms, which are reported in the literature. Furthermore, transplanckian effects do not necessarily leave an imprint on the spectrum of cosmic perturbations generated during inflation.