We discuss formation of an $S$-wave bound state in finite volume on the basis of Lüscher’s phase-shift formula. It is found that although a bound-state pole condition is fulfilled only in the infinite-volume limit, its modification by the finite-size corrections is exponentially suppressed by the spatial extent $L$ in a finite box $L^3$. We also confirm that the appearance of the $S$-wave bound state is accompanied by an abrupt sign change of the $S$-wave scattering length even in finite volume through numerical simulations. This distinctive behavior may help us to distinguish the loosely bound state from the lowest energy level of the scattering state in finite-volume simulations.

Hybrid mesons are exotic mesons in which the color field is not in its ground state. Their understanding deserves interest from a theoretical point of view, because it is intimately related to nonperturbative aspects of QCD. In this work, we analyze and compare two different descriptions of hybrid mesons, namely, a two-body $q\overline{q}$ system with an excited string, or a three-body $q\overline{q}g$ system. In particular, we show that the constituent gluon approach is equivalent to an effective excited string in the heavy hybrid sector. Instead of a numerical resolution, we use the auxiliary field technique. It allows us to find simplified analytical mass spectra and wave functions, and still leads to reliable qualitative predictions. We also investigate the light hybrid sector, and found a mass for the lightest hybrid meson which is in satisfactory agreement with lattice QCD and some effective models.

We investigate the $1/2$-BPS Wilson–’t Hooft loops in $\mathcal{N}=4$ super-Yang-Mills theory. We use the bulk D-brane with both electric and magnetic charges to calculate the all-genus contribution of the circular loops. The expectation values of Wilson–’t Hooft loops are in perfect agreement with the result through supersymmetric condition and duality transformation in the gauge theory.

We investigate the quantum motion of a neutral Dirac particle bouncing on a mirror in curved spacetime. We consider different geometries: Rindler, Kasner-Taub, and Schwarzschild, and show how to solve the Dirac equation by using geometrical methods. We discuss, in a first-quantized framework, the implementation of appropriate boundary conditions. This leads us to consider a Robin boundary condition that gives the quantization of the energy, the existence of bound states and of critical heights at which the Dirac particle bounces, extending the well-known results established from the Schrödinger equation. We also allow for a nonminimal coupling to a weak magnetic field. The problem is solved in an analytical way on the Rindler spacetime. In the other cases, we compute the energy spectrum up to the first relativistic corrections, exhibiting the contributions brought by both the geometry and the spin. These calculations are done in two different ways. On the one hand, using a relativistic expansion and, on the other hand, with Foldy-Wouthuysen transformations. Contrary to what is sometimes claimed in the literature, both methods are in agreement, as expected. Finally, we make contact with the GRANIT experiment. Relativistic effects and effects that go beyond the equivalence principle escape the sensitivity of such an experiment. However, we show that the influence of a weak magnetic field could lead to observable phenomena.

We study instanton solutions and superpotentials for the large number of vacua of the plane-wave matrix model and a $2+1$ dimensional Super Yang-Mills theory on $R\times S^2$ with 16 supercharges. We get the superpotential in the weak-coupling limit from the gauge theory description. We study the gravity description of these instantons. Perturbatively, with respect to a background, they are Euclidean branes wrapping cycles in the dual gravity background. Moreover, the superpotential can be given by the energy of the electric charge system characterizing each vacuum. These charges are interpreted as the eigenvalues of matrices from a reduction for the $1/8$ BPS sector of the gauge theories. We also discuss qualitatively the emergence of the extra spatial dimensions appeared on the gravity side.

The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.

The question whether the center vortex picture of the strongly interacting vacuum can encompass the infrared dynamics of both $SU(2)$ as well as $Sp(2)$ Yang-Mills theory is addressed. These two theories contain the same center vortex degrees of freedom, and yet exhibit deconfinement phase transitions of different order. This is argued to be caused by the effective action governing the vortices being different in the two cases. To buttress this argument, a random vortex world-surface model is constructed which reproduces available lattice data characterizing $Sp(2)$ Yang-Mills confinement properties. A new effective action term which can be interpreted in terms of a vortex stickiness serves to realize a first-order deconfinement phase transition, as found in $Sp(2)$ Yang-Mills theory. Predictions are given for the behavior of the spatial string tension at finite temperatures.

We use a dynamical systems approach to investigate Bianchi type I and II universes in quadratic theories of gravity. Because of the complicated nature of the equations of motion we focus on the stability of exact solutions and find that there exists an isotropic Friedmann-Robertson-Walker (FRW) universe acting as a past attractor. This may indicate that there is an isotropization mechanism at early times for these kind of theories. We also discuss the Kasner universes, elucidate the associated center manifold structure, and show that there exists a set of nonzero measure which has the Kasner solutions as a past attractor. Regarding the late-time behavior, the stability shows a dependence of the parameters of the theory. We give the conditions under which the de Sitter solution is stable and also show that for certain values of the parameters there is a possible late-time behavior with phantomlike behavior. New types of anisotropic inflationary behavior are found which do not have counterparts in general relativity.

We study gravitationally collapsing models of pressureless dust, fluids with pressure, and the generalized Chaplygin gas (GCG) shell in $(2+1)$-dimensional spacetimes. Various collapse scenarios are investigated under a variety of the background configurations such as anti-de Sitter (AdS) black hole, de Sitter (dS) space, flat and AdS space with a conical deficit. As with the case of a disk of dust, we find that the collapse of a dust shell coincides with the Oppenheimer-Snyder type collapse to a black hole provided the initial density is sufficiently large. We also find—for all types of shell—that collapse to a naked singularity is possible under a broad variety of initial conditions. For shells with pressure this singularity can occur for a finite radius of the shell. We also find that GCG shells exhibit diverse collapse scenarios, which can be easily demonstrated by an effective potential analysis.

Motivated by landscape models in string theory, cosmic nuclear evolution is analyzed allowing the standard model Higgs expectation value $w$ to take values different from that in our world ($w\equiv 1$), while holding the Yukawa couplings fixed. Thresholds are estimated, and astrophysical consequences are described, for several sensitive dependences of nuclear behavior on $w$. The dependence of the neutron-proton mass difference on $w$ is estimated based on recent calculations of strong isospin symmetry breaking, and is used to derive the threshold of neutron-stable worlds, $w\approx 0.6\pm 0.2$. The effect of a stable neutron on nuclear evolution in the big bang and stars is shown to lead to radical differences from our world, such as a predominance of heavy $r$-process and $s$-process nuclei and a lack of normal galaxies, stars, and planets. Rough estimates are reviewed of $w$ thresholds for deuteron stability and the $pp$ and $pep$ reactions dominant in many stars. A simple model of nuclear resonances is used to estimate the $w$ dependence of overall carbon and oxygen production during normal stellar nucleosynthesis; carbon production is estimated to change by a fraction $\approx 15(1-w)$. Radical changes in astrophysical behavior seem to require changes in $w$ of more than a few percent, even for the most sensitive phenomena.

To study the deconfining phase transition at nonzero temperature, I outline the perturbative construction of an effective theory for straight, thermal Wilson lines. Certain large, time dependent gauge transformations play a central role. They imply the existence of interfaces, which can be used to determine the form of the effective theory as a gauged, nonlinear sigma model of adjoint matrices. Especially near the transition, the Wilson line may undergo a Higgs effect. As an adjoint field, this can generate eigenvalue repulsion in the effective theory.

We study one-loop quantum corrections of a compactified Abelian $5d$ gauge field theory. We use a cut-off regularization procedure which respects the symmetries of the model, i.e. gauge invariance, exhibits the expected powerlike divergences and therefore allows the derivation of power-law behavior of the effective $4d$ gauge coupling in a coherent manner.

The colored $SU(2{)}_L$-singlet heavy $T$-quark is one of the most crucial ingredients in little Higgs models, which is introduced to cancel the largest contribution of the standard model (SM) top quark to the Higgs boson mass at one-loop level. In two representative little Higgs models, the littlest Higgs model and the $SU(3)$ simplest Higgs model, we comprehensively study the single heavy $T$-quark production at Large Hadron Collider (LHC). After presenting the possibility of relatively light ($\sim 500\mathrm{GeV}$) $T$-quark in the simplest little Higgs model, we consider all the relevant processes, the $2\to 2$ process of $qb\to q^{\prime }T$, the $2\to 3$ process of $qg\to q^{\prime }T\overline{b}$, the $s$-channel process of $q{\overline{q}}^{\prime }\to T\overline{b}$, and the gluon-fusion process of $gg\to T\overline{t}$. We found that the $2\to 3$ process can be quite important, as its cross section is about 30% of the $2\to 2$ one and it is dominant in high $p_T$ distributions. The $s$-channel and the gluon-fusion processes also show distinctive features in spite of their suppressed cross sections. In the gluon-fusion process of the simplest little Higgs model, for example, the pseudoscalar contribution is rather dominant over the Higgs contribution for relatively light $M_T$.

We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical counterpart of this system. A similar analysis is then done for an alike, but nonsupersymmetric, system. The comparison of these classical and quantum results may serve as a suggestion about classical manifestations of supersymmetry.

The discovery of supersymmetric (SUSY) particles at the Large Hadron Collider (LHC) has been studied for models where the squarks and gluino are much heavier than the lightest supersymmetric particle. In this paper, we investigate SUSY discovery in models with a degenerate mass spectrum up to $m_{\mathrm{LSP}}\lesssim 0.7m_{\tilde{q}}$. Such a mass spectrum is predicted in a certain parameter region of the mixed modulus anomaly mediation model. We find that the effective transverse mass of the signal for the degenerate parameters shows a distribution similar to that of the background. Experimental sensitivity to the SUSY particles at the LHC therefore depends on the uncertainty of the background in this class of model. We also find that the SUSY signal shows an interesting correlation between $M_{\mathrm{eff}}$ and ${\mathrm{E̸}}_{\mathrm{T}}$ which may be used to better determine the signal region and enhance the $\mathrm{S}/\mathrm{N}$ ratio even if the sparticle masses are rather degenerate. This correlation is universal for models with new heavy colored particles decaying into visible particles and a stable neutral dark matter.

We describe a calculation of the $\mathcal{O}({\alpha }_s^2)$ QCD corrections to the fully differential cross section for $W$ and $Z$ boson production in hadronic collisions. The result is fully realistic in that it includes spin correlations, finite width effects, $\gamma -Z$ interference and allows for the application of arbitrary cuts on the leptonic decay products of the $W$ and $Z$. We have implemented this calculation into a numerical program. We demonstrate the use of this code by presenting phenomenological results for several future LHC analyses and recent Tevatron measurements, including the $W$ cross section in the forward rapidity region and the central over forward cross section ratio.

We discuss the form and construction of general color singlet heavy particle-antiparticle pair production currents for arbitrary quantum numbers, and issues related to evanescent spin operators and scheme dependences in nonrelativistic QCD in $n=3-2ϵ$ dimensions. The anomalous dimensions of the leading interpolating currents for heavy quark and colored scalar pairs in arbitrary ${}^{2S+1}L_J$ angular-spin states are determined at next-to-leading order in the nonrelativistic power counting.

We present a calculation of the loop-induced processes $gg\to HH$ and $gg\to HHH$, and investigate the observability of multi-Higgs boson production at the CERN Large Hadron Collider (LHC) in the Standard Model (SM) and beyond. While the SM cross sections are too small to allow observation at the LHC, we demonstrate that physics beyond the SM can lead to amplified, observable cross sections. Furthermore, the applicability of the heavy top quark approximation in two- and three-Higgs boson production is investigated. We conclude that multi-Higgs boson production at the SuperLHC is an interesting probe of Higgs sectors beyond the SM and warrants further study.

Heavy singlet neutrinos admit Majorana masses which are not possible for the Standard Model particles. This suggest new possibilities for generating the masses and mixing angles of light neutrinos. We present a model of neutrino physics which combines the source of lepton-number violation with the flavor symmetry responsible for the hierarchy in the charged lepton and quark sector. This is accomplished by giving the scalar field effecting the lepton-number violation a nonzero charge under the horizontal flavor symmetry. We find an economical model which is consistent with the measured values of the atmospheric and solar neutrino mass-squares and mixing angles.