We study the effect of variations of the electromagnetic coupling on the process of generation of primordial magnetic fields. We find that only through a significant growth of the electromagnetic coupling can minimum seed fields be produced. We also show that, if through some process in the early Universe the photon acquires a mass that leads, thanks to inflation, to the generation of primordial magnetic fields, then the influence of variations of the electromagnetic coupling amounts essentially to the results due to the photon effective mass alone.

We discuss the effects of a possible time variation of the Newton constant $G_{\mathrm{N}}$ on light elements production in big bang nucleosynthesis (BBN). We provide analytical estimates for the dependence of primordial abundances on the value of the Newton constant during BBN. The accuracy of these estimates is then tested by numerical methods. Moreover, we determine numerically the response of each element to an arbitrary time-dependent modification of the early universe expansion rate. Finally, we determine the bounds on possible variations of $G_{\mathrm{N}}$ which can be obtained from the comparison of theoretical predictions and observational data.

Generic models of cosmological inflation and the recently proposed scenarios of a recycling universe and the string theory landscape predict spacetimes whose global geometry is a stochastic, self-similar fractal. To visualize the complicated causal structure of such a universe, one usually draws a conformal (Carter-Penrose) diagram. I develop a new method for drawing conformal diagrams, applicable to arbitrary 1+1-dimensional spacetimes. This method is based on a qualitative analysis of intersecting lightrays and thus avoids the need for explicit transformations of the spacetime metric. To demonstrate the power and simplicity of this method, I present derivations of diagrams for spacetimes of varying complication. I then apply the lightray method to three different models of an eternally inflating universe (scalar-field inflation, recycling universe, and string theory landscape) involving the nucleation of nested asymptotically flat, de Sitter and/or anti-de Sitter bubbles. I show that the resulting diagrams contain a characteristic fractal arrangement of lines.

We consider a lattice formulation of the four-dimensional $N=1$ Wess-Zumino model that uses the Ginsparg-Wilson relation. This formulation has an exact supersymmetry on the lattice. We show that the corresponding Ward-Takahashi identity is satisfied, both at fixed lattice spacing and in the continuum limit. The calculation is performed in lattice perturbation theory up to order $g^2$ in the coupling constant. We also show that this Ward-Takahashi identity determines the finite part of the scalar and fermion renormalization wave functions which automatically leads to restoration of supersymmetry in the continuum limit. In particular, these wave functions coincide in this limit.

Is the relatively isolated member of the neutrino mass spectrum heavier or lighter than the two closely-spaced members? This question—the character of the neutrino mass hierarchy—is of great theoretical interest. All previously identified experiments for addressing it via neutrino oscillations require that the currently unknown size of the $U_{e3}$ element of the leptonic mixing matrix (parameterized by the unknown ${\theta }_{13}$ mixing angle) be sufficiently large, and will utterly fail in the limit ${\theta }_{13}\to 0$. For this reason, we explore alternative oscillation approaches that would still succeed even if ${\theta }_{13}$ vanishes. We identify several alternatives that require neither a nonzero $|U_{e3}|$ nor the presence of significant matter effects (even if the latter are unavoidable in the case of long-baseline, Earth-based experiments). All include multiple percent-level neutrino oscillation measurements, usually involving muon-neutrino (or antineutrino) disappearance and very long baselines. We comment on the degree of promise that these alternative approaches show.

If it can be ascertained experimentally that the $3\times 3$ Majorana neutrino mass matrix ${\mathcal{M}}_{\nu }$ has vanishing determinants for one or more of its $2\times 2$ submatrices, it may be interpreted as supporting evidence for the theoretically well-known canonical seesaw mechanism. I show how these two things are connected and offer a realistic ${\mathcal{M}}_{\nu }$ with two zero subdeterminants as an example.

There is in the literature a number of papers addressing the stochastic background of gravitational waves (GWs) generated by an ensemble of astrophysical sources. The main ingredient in such studies is the so called star formation rate density (SFRD), which gives the density of stars formed per unit time. Some authors argue, however, that there is, in the equation that determines the amplitude of the stochastic background of GWs, an additional $(1+z)$ term dividing the SFRD, which would account for the effect of cosmic expansion onto the time variable. We argue here that the inclusion of this additional term is wrong. In order to clarify where the inclusion of the $(1+z)$ term is really necessary, we briefly discuss the calculation of event rates in the study of GRBs (gamma ray bursts) from cosmological origin.

We calculate and display the primordial light-element abundances as a function of a neutrino degeneracy parameter $\xi$ common to all flavors. It is the only unknown parameter characterizing the thermal medium at the primordial nucleosynthesis epoch. The observed primordial helium abundance $Y_{\mathrm{p}}$ is the most sensitive cosmic “leptometer.” Adopting the conservative $Y_{\mathrm{p}}$ error analysis of Olive and Skillman implies $-0.04\lesssim \xi \lesssim 0.07$ whereas the errors stated by Izotov and Thuan imply $\xi =0.0245\pm 0.0092$ ($1\sigma$). Improved determinations of the baryon abundance have no significant impact on this situation. A determination of $Y_{\mathrm{p}}$ that reliably distinguishes between a vanishing or nonvanishing $\xi$ is a crucial test of the cosmological standard assumption that sphaleron effects equilibrate the cosmic lepton and baryon asymmetries.

We consider defect composite operators in a defect superconformal field theory obtained by inserting an ${\mathrm{AdS}}_4\times {\mathrm{S}}^2$-brane in the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ background. The one-loop dilatation operator for the scalar sector is represented by an integrable open spin chain. We give a description to construct coherent states for the open spin chain. Then, by evaluating the expectation value of the Hamiltonian with the coherent states in a long operator limit, a Landau-Lifshitz type of sigma model action is obtained. This action is also derived from the string action and hence we find a complete agreement in both super Yang-Mills and string sides. We see that an $\mathrm{SO}(3{)}_{\mathrm{H}}$ pulsating string solution is included in the action and its energy completely agrees with the result calculated in a different method. In addition, we argue that our procedure would be applicable to other AdS-brane cases.

We propose various ways of adding mass terms to three-dimensional twistor string theory. We begin with a review of mini-twistor space—the reduction of $D=4$ twistor space to $D=3$. We adapt the two proposals for twistor string theory, Witten’s and Berkovits’s, to $D=3$ super Yang-Mills theory. In Berkovits’s model, we identify the enhanced R symmetry. We then construct B-model topological string theories that, we propose, correspond to $D=3$ Yang-Mills theory with massive spinors and massive and massless scalars in the adjoint representation of the gauge group. We also analyze the counterparts of these constructions in Berkovits’s model. Some of our constructions can be lifted to $D=4$, where infinitesimal mass terms correspond to vacuum expectation values of certain superconformal gravity fields.

We investigate the ultrarelativistic boost of the five-dimensional Emparan-Reall nonrotating black ring. Following the classical method of Aichelburg and Sexl, we determine the gravitational field generated by a black ring moving “with the speed of light” in an arbitrary direction. In particular, we study in detail two different boosts along axes orthogonal and parallel to the plane of the ring circle, respectively. In both cases, after the limit one obtains a five-dimensional impulsive $pp$-wave propagating in Minkowski spacetime. The curvature singularity of the original static spacetime becomes a singular source within the wave front, in the shape of a ring or a rod according to the direction of the boost. In the case of an orthogonal boost, the wave front contains also a remnant of the original disk-shaped membrane as a component of the Ricci tensor (which is everywhere else vanishing). We also analyze the asymptotic properties of the boosted black ring at large spatial distances from the singularity, and its behavior near the sources. In the limit when the singularity shrinks to a point, one recovers the well-known five-dimensional analogue of the Aichelburg-Sexl monopole solution.

In this paper we present the renormalization group equations to one-loop order for all the parameters of two supersymmetric left-right theories that are softly broken. Both models are based upon the gauge group $SU(3{)}^c\times SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$ and both contain an arbitrary number of bidoublets as well as singlets; however, one model uses doublets to break $SU(2{)}_R$ and the other uses triplets.

Within the framework of quenched lattice QCD and using $O(a)$ improved Wilson fermions and nonperturbative renormalization, a high statistics computation of low moments of the unpolarized nucleon structure functions is given. Particular attention is paid to the chiral and continuum extrapolations.

We analyze heavy quark free energies in 2-flavor QCD at finite temperature and the corresponding heavy quark potential at zero temperature. Static quark-antiquark sources in color singlet, octet and color averaged channels are used to probe thermal modifications of the medium. The temperature dependence of the running coupling, ${\alpha }_{qq}(r,T)$, is analyzed at short and large distances and is compared to zero temperature as well as quenched calculations. In part, we also compare our results to recent findings in 3-flavor QCD. We find that the characteristic length scale below which the running coupling shows almost no temperature dependence is almost twice as large as the Debye screening radius. Our analysis supports recent findings which suggest that ${\chi }_c$ and ${\psi }^{\prime }$ are suppressed already at the (pseudo) critical temperature and thus give a probe for quark gluon plasma production in heavy ion collision experiments, while $J/\psi$ may survive the transition and will dissolve at higher temperatures.

We consider the role of the velocity in Lorentz-violating fermionic quantum theory, especially emphasizing the nonrelativistic regime. Information about the velocity will be important for the kinematical analysis of scattering and other problems. Working within the minimal standard model extension, we derive new expressions for the velocity. We find that generic momentum and spin eigenstates may not have well-defined velocities. We also demonstrate how several different techniques may be used to shed light on different aspects of the problem. A relativistic operator analysis allows us to study the behavior of the Lorentz-violating Zitterbewegung. Alternatively, by studying the time evolution of Gaussian wave packets, we find that there are Lorentz-violating modifications to the wave packet spreading and the spin structure of the wave function.

We investigate the vacuum structure of pure $SU(N)$ $\mathcal{N}=1$ super Yang-Mills theory. The theory is expected to possess $N$ vacua with associated domain walls. We show that the newly extended version of the low energy effective Lagrangian for super Yang-Mills theory supports the Bogomol’nyi-Prasad-Sommerfield (BPS) domain wall solutions associated with any two vacua aligned with the origin of the moduli space. For the two color theory the domain wall analysis is complete. We also find new non-BPS domain wall solutions connecting any two vacua of the underlying $SU(N)$ super Yang-Mills theory not necessarily aligned. When two vacua are aligned with the origin of the moduli space these solutions are the BPS ones. We also discuss the generic BPS domain wall solutions connecting any two vacua within the extended Veneziano-Yankielowicz theory.

Two families of $SO(2n)$ Higgs models in $2n$ dimensional spacetimes are presented. The energies corresponding to the monopole solutions of all these models saturate the Bogomol’nyi bound. One of these families arises from the dimensional reduction of higher dimensional Yang-Mills systems while the generic models are constructed only with a view to saturating Bogomol’nyi-Prasad-Sommerfield monopole (BPS) bounds. The $n=2$ member of each family coincides with the usual $SU(2)$ Yang-Mills–Higgs system without Higgs potential. All models support BPS “monopole” solutions. While all the monopoles are BPS, only the “dyons” of the dimensionally descended models are also BPS, the electrically charged solutions of the generic models not saturating a Bogomol’nyi bound.

We investigate the strong coupling region of the topological sector of the two-dimensional ${\varphi }^4$ theory. Using discrete light cone quantization, we extract the masses of the lowest few excitations and observe level crossings. To understand this phenomena, we evaluate the expectation value of the integral of the normal ordered ${\varphi }^2$ operator and we extract the number density of constituents in these states. A coherent state variational calculation confirms that the number density for low-lying states above the transition coupling is dominantly that of a kink-antikink-kink state. The Fourier transform of the form factor of the lowest excitation is extracted which reveals a structure close to a kink-antikink-kink profile. Thus, we demonstrate that the structure of the lowest excitations becomes that of a kink-antikink-kink configuration at moderately strong coupling. We extract the critical coupling for the transition of the lowest state from that of a kink to a kink-antikink-kink. We interpret the transition as evidence for the onset of kink condensation which is believed to be the physical mechanism for the symmetry restoring phase transition in two-dimensional ${\varphi }^4$ theory.

We propose a method to probe the phenomenological nature of dark energy which makes no assumptions about the evolution of its energy density. We exemplify this method with a test for a super-acceleration phase of the universe i.e., a phase when the dark energy density grows as the universe expands. We show how such a phase can be detected by combining SNIa (SNAP-like) and CMB (Planck) data without making any assumptions about the evolution of the dark energy equation of state, or about the value of the matter density parameter.