We introduce a dynamical matrix model where the matrix is interpreted as a Hamiltonian representing interaction of a bosonic system with a single fermion. We show how a system of second-quantized fermions influences the ground state of the whole system by producing a gap between the highest eigenvalue of the occupied single-fermion states and the lowest eigenvalue of the unoccupied single-fermion states. We describe the development of the gap in both the strong and weak coupling regimes, while for the intermediate coupling strength we expect formation of homolumo kinks.

We construct the generating functional for the light-cone superfield amplitudes in a chiral momentum superspace. It generates the $n$-point particle amplitudes which on shell are equivalent to the covariant ones. Based on the action depending on the unconstrained light-cone chiral scalar superfield, this functional provides a regular $d=4$ quantum field theory path integral derivation of the Nair-type amplitude constructions. By performing a Fourier transform into the light-cone chiral coordinate superspace we find that the quantum corrections to the superfield amplitudes with $n$ legs are nonlocal in transverse directions for the diagrams with the number of loops smaller than at least $n+3$. This suggests the reason why UV infinities, which are proportional to local vertices, cannot appear at least before 7 loops in the light-cone supergraph computations. Using the $E_{7(7)}$ symmetry we argue that the light-cone supergraphs predict all-loop finiteness of $d=4$ $\mathcal{N}=8$ supergravity.

We consider scalar-tensor theories of gravity extended by pseudoscalar couplings to matter and gauge fields and derive constraints on the $CP$-odd combinations of scalar and pseudoscalar couplings from laboratory spin precession experiments and from the evolution of photon polarization over cosmological distances. We show the complementary character of local and cosmological constraints, and derive novel bounds on the pseudoscalar couplings to photons from the laboratory experiments. It is also shown that the more accurate treatment of the spin content of nuclei used in the spin precession experiments allows us to tighten bounds on Lorentz-violating backgrounds coupled to the proton spin.

Spherically symmetric thin-shell wormholes are studied within the framework of Einstein-Born-Infeld theory. We analyze the exotic matter content, and find that for certain values of the Born-Infeld parameter the amount of exotic matter on the shell can be reduced in relation to the Maxwell case. We also examine the mechanical stability of the wormhole configurations under radial perturbations preserving the spherical symmetry. In addition, in the Appendix the repulsive or attractive character of the wormhole geometries is briefly discussed.

We present the black hole solutions and analyze their properties in the superstring effective field theory with the Gauss-Bonnet curvature correction terms. We find qualitative differences in our results from those obtained in the truncated model in the Einstein frame. The main difference in our model from the truncated one is that the existence of a turning point in the mass-area curve, the mass-entropy curve, and the mass-temperature curve in five and higher dimensions, where we expect a change of stability. We also find a mass gap in our model, where there is no black hole solution. In five dimensions, there exists a maximum black hole temperature and the temperature vanishes at the minimum mass, which is not found in the truncated model.

We study the consistency of a model which includes torsion as well as the metric as dynamical fields and has massive spin-2 particle in its spectrum. It is known that this model is tachyon free and ghost free in Minkowski background. We show that this property remains valid and no other pathologies emerge in de Sitter and anti-de Sitter backgrounds, with some of our results extending to arbirary Einstein space backgrounds. This suggests that the model is consistent, at least at the classical level, unlike, e.g., the Fierz-Pauli theory.

We study the spectrum ${\mathcal{P}}_{\zeta }$ and bispectrum $B_{\zeta }$ of the primordial curvature perturbation $\zeta$ when the latter is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree-level terms [both (either) in ${\mathcal{P}}_{\zeta }$ and (or) in $B_{\zeta }$] and vice versa. The level of non-Gaussianity in the bispectrum, $f_{\mathrm{NL}}$, is calculated and related to the level of statistical anisotropy in the power spectrum, $g_{\zeta }$. For very small amounts of statistical anisotropy in the power spectrum, the level of non-Gaussianity may be very high, in some cases exceeding the current observational limit.

We explore supersymmetry breaking in the light of a rich fixed-point structure of two-dimensional supersymmetric Wess-Zumino models with one supercharge using the functional renormalization group. We relate the dynamical breaking of supersymmetry to a renormalization group relevant control parameter of the superpotential which is a common relevant direction of all fixed points of the system. Supersymmetry breaking can thus be understood as a quantum phase transition analogous to similar transitions in correlated fermion systems. Supersymmetry gives rise to a new superscaling relation between the critical exponent associated with the control parameter and the anomalous dimension of the field—a scaling relation which is not known in standard spin systems.

We analyze the decays to muons of a light dilaton produced via vector boson fusion at the LHC. We investigate models in which the electroweak symmetry breaking is triggered by a spontaneously broken, approximately conformal sector. Taking into account the possibility of shifts in the dilaton Yukawa couplings to muons, we find a rather promising scenario for the conformal model search in the channel, with the possibility for a dilaton discovery at a delivered luminosity of $100{\mathrm{fb}}^{-1}$ at the LHC or, alternatively, for an extension of the exclusion zone in the model parameter space, until now fixed by the Tevatron.

In the framework of warped extra dimension models addressing the gauge hierarchy problem, we consider the Randall-Sundrum (RS) scenario under the usual hypothesis of a bulk custodial symmetry. It is shown in detail that there can exist large corrections to the Higgs boson vacuum expectation value (VEV) induced by mixings of the gauge bosons with their Kaluza-Klein (KK) excitations. The connection with electroweak precision tests is developed. A noteworthy result is that the correct treatment of the Higgs VEV leads to an increase of the lower limit at 95% C.L. on KK masses that can reach $+30\%$ (from usually accepted values). For a Higgs mass $120\le m_h\le 150\mathrm{GeV}$, the obtained limit (from updated precision data) on the first KK gauge boson mass lies in the range 3.3–4.0 TeV. The VEV corrections also play a central role in the corrections to the Higgs couplings. We find possibly substantial RS corrections to the various Higgs couplings able to affect its phenomenology, starting with a Higgs discovery at the LHC more challenging than in the standard model (SM). The deviations to the Higgs production/decay rates found in RS will be testable at the ILC as well as at LHC. Such RS signatures could even be used at the ILC to discriminate among several models beyond the SM. Finally, the possibility of a light Higgs boson ($m_h\simeq 99\mathrm{GeV}$) interpreting the excess at $2.3\sigma$ observed at LEP2 is pointed out.

Diverse mass and mixing patterns between the quarks and leptons makes it challenging to construct a simple grand unified theory of flavor. We show that SO(10) supersymmetry grand unified theories with type II seesaw mechanism giving neutrino masses provide a natural framework for addressing this issue. A simple ansatz that the dominant Yukawa matrix (the $\mathbf{10}$-Higgs coupling to matter) has rank one appears to simultaneously explain both the large lepton mixings as well as the observed quark flavor hierarchy in these models. A testable prediction of this ansatz is the neutrino mixing, $U_{e3}$, which should be observable in planned long baseline experiments.

The imbalance of dijets produced in hadronic collisions has been used to extract the average transverse momentum of partons inside the hadrons. In this paper we discuss new contributions to the dijet imbalance that could complicate or even hamper this extraction. They are due to polarization of initial state partons inside unpolarized hadrons that can arise in the presence of nonzero parton transverse momentum. Transversely polarized quarks and linearly polarized gluons produce specific azimuthal dependences of the two jets that in principle are not suppressed. Their effects cannot be isolated just by looking at the angular deviation from the back-to-back situation; rather they enter jet broadening observables. In this way they directly affect the extraction of the average transverse momentum of unpolarized partons that is thought to be extracted. We discuss appropriately weighted cross sections to isolate the additional contributions.

In this work we calculate the branching ratios of semileptonic and nonleptonic decays of ${\Lambda }_b$ into light baryons ($p$ and $\Lambda$), as well as the measurable asymmetries which appear in the processes, in the light-front quark model. In the calculation, we adopt the diquark picture and discuss the justifiability of applying the picture in our case. Our result on the branching ratio of ${\Lambda }_b\to \Lambda +J/\psi$ is in good agreement with the data. More predictions are made in the same model and the results will be tested in the future experiments which will be conducted at the Large Hadron Collider beauty and even the International Linear Collider.

We study the effects of the perturbation, which violates the permutation symmetry of three Majorana neutrinos but preserves the well-known (23) interchange symmetry. This is done in the presence of an arbitrary Majorana phase $\psi$, which serves to ensure the degeneracy of the three neutrinos at the unperturbed level.

We study multiphoton effects in quantum electrodynamics in lepton photoproduction on heavy nuclei and nuclear medium at high energies. We are interested in energy, charge density, and nuclear geometry dependence of the cross sections. We use the impact parameter representation that allows us to reduce the problem of photoproduction to the problem of propagation of electric dipoles in the nuclear Coulomb field. In the framework of the Glauber model we resum an infinite series of multiphoton amplitudes corresponding to multiple rescattering of the electric dipole on the nucleus. We find that unitarity effects arising due to multiphoton interactions are small and energy independent for scattering on a single nucleus, whereas in the case of macroscopic nuclear medium they saturate the geometric limit of the total cross section. We discuss an analogy between nuclear medium and intense laser beams.

In extra-dimensional scenarios oscillations between active and sterile neutrinos can be governed by a new resonance in the oscillation amplitude. This resonance results when cancellation occurs between two phase differences, the usual kinematic one coming from the neutrino mass-squared difference, and a geometric one coming from the difference in travel times of the sterile neutrino through the bulk relative to the active neutrino confined to the brane. In this work we introduce a specific metric for the brane-bulk system, from which we explicitly derive extra-dimensional geodesics for the sterile neutrino, and ultimately the oscillation probability of the active-sterile two-state system. We find that for an asymmetrically warped metric, the resonance condition involves both the neutrino energy $E$ and the travel distance $L$ on the brane. In other words, the resonant energy may be viewed as baseline dependent. We show that to a good approximation, the resonance condition is not on $E$ or on $L$, but rather on the product $LE$. The model is rich in implications, including the possibility of multiple solutions to the resonance condition, with ramifications for existing data sets, e.g., LSND and MiniBooNE. Some phenomenology with these brane-bulk resonances is discussed.

We construct exact two-dimensional conformal field theories, corresponding to closed string tachyon and metric profiles invariant under shifts in a null coordinate, which can be constructed from any two-dimensional renormalization group flow. These solutions satisfy first order equations of motion in the conjugate null coordinate. The direction along which the tachyon varies is identified precisely with the world sheet scale, and the tachyon equations of motion are the renormalization group flow equations.

We construct a massive non-Abelian $\mathcal{N}=1$ supersymmetric Yang-Mills theory on ${\mathbb{R}}^3$. This is achieved by using a nonlocal gauge and a Poincare invariant mass term for gluons due to Nair. The underlying supersymmetry algebra is shown to be a noncentral extension of the Poincare algebra by the spacetime rotation group $so(3)$. The incorporation of Chern-Simons couplings in the formalism is also presented. The dimensional reduction of the gauge theory and the supersymmetry algebra is related to a massive $\mathcal{N}=2$ matrix quantum mechanics based on Euclidean ${\mathrm{Clifford}}_2(\mathbb{R})$.

In the framework of phantom quintessence cosmology, we use the Noether Symmetry Approach to obtain general exact solutions for the cosmological equations. This result is achieved by the quintessential (phantom) potential determined by the existence of the symmetry itself. A comparison between the theoretical model and observations is worked out. In particular, we use type Ia supernovae and large-scale structure parameters determined from the 2-degree Field Galaxy Redshift Survey and from the Wide part of the VIMOS-VLT Deep Survey ). It turns out that the model is compatible with the presently available observational data. Moreover we extend the approach to include radiation. We show that it is compatible with data derived from recombination and it seems that quintessence do not affect nucleosynthesis results.

We show that three-dimensional massive gravity admits Lifshitz metrics with generic values of the dynamical exponent $z$ as exact solutions. At the point $z=3$, exact black hole solutions that are asymptotically Lifshitz arise. These spacetimes are three-dimensional analogues of those that were recently proposed as gravity duals for anisotropic scale invariant fixed points.