Anomaly puzzle, curved-spacetime spinor Hamiltonian, and string phenomenology

The advent of the Large Hadron Collider (LHC) and the continuing influx of cosmological data could inject new energy to the relatively quiet field of string theory. Predictions from string models based on large extra dimensions could be tested in the energy range within the reach of the LHC or other upcoming experiments. In the first part of this dissertation, we study three different aspects of string phenomenology.;First, we consider extensions of the Standard Model based on open strings ending on D-branes, in which gauge bosons exist as strings attached to stacks of D-branes, and chiral matter as strings stretching between intersecting D-branes. Under the assumptions that the fundamental string scale is in the TeV range and the theory is weakly coupled, we study the complementary signals of low mass superstrings at the proposed electron-positron facility (CLIC), in e+e- and gammagamma collisions. We examine all relevant four-particle amplitudes evaluated at the center of mass energies near the mass of lightest Regge excitations and extract the corresponding pole terms. We show that, in the minimal extension of the Standard Model, gammagamma → e+ e- scattering proceeds only through a spin-2 Regge state. We estimate that for this particular channel, string scales as high as 4 TeV can be discovered at the 11sigma level with the first fb -1 of data collected at a center-of-mass energy ≈ 5 TeV.;Next, we consider string realizations of the Randall-Sundrum effective theory and explore the search for the lowest massive Regge excitation of the gluon and of the extra (color singlet) gauge boson inherent of D-brane constructions. In these curved backgrounds, the higher-spin Regge recurrences of Standard Model fields localized near the IR bran are warped down to close to the TeV range and hence can be produced at collider experiments. We make use of four gauge boson amplitudes evaluated near the first Regge pole to determine the discovery potential of LHC. We find that with an integrated luminosity of 100 fb-1, the 5sigma discovery reach for pp → dijet can be as high as 4.7 TeV. We also study the ratio of dijet mass spectra at small and large scattering angles. We show that with the first fb-1 such a ratio can probe lowest-lying Regge states for masses ∼ 3 TeV.;Finally, we propose that the 3.2sigma excess at about 140 GeV in the dijet mass spectrum of W + jets reproted by the CDF Collaboration originates in the decay of a leptophobic Z' that can be related to the U(1) symmetries inherent of D-brane models.;In the second part, we discuss several points that may help to clarify some questions that remain about the anomaly puzzle in N = 1 supersymmetric Yang-Mills theory. The anomaly puzzle concerns the question of whether there is a consistent way in the quantized theory to put the R-current and the stress tensor in a single supermultiplet called the supercurrent. It was proposed that the classically conserved supercurrent bifurcates into two supercurrents having different anomalies in the quantum regime. The most interesting result we obtain is an explicit expression for the lowest component of one of the two supercurrents, namely the supercurrent that has the energy-momentum tensor as one of its components. This lowest component is an energy-dependent linear combination of two chiral currents, one of those being the lowest component of the other supercurrent, namely, the R-current. Therefore, we conclude that there is no consistent way to construct a single supercurrent multiplet that contains the R-current and the stress tensor in the straightforward way originally proposed. We also discuss and try to clarify some technical points in the derivations of the two supercurrents in the literature. These latter points concern the significance of the infrared contributions to the NSVZ beta-function and the role of the equations of motion in deriving the two supercurrents.;In the third part, we investigate the issue that the Dirac Hamiltonian of a spin-½ particle in a curved background appears to be non-hermitian (with respect to the conserved scalar product) when the metric is time-dependent. Here, we show that this non-hermiticity results from a time dependence of the position eigenstates that enter into the Schrodinger wave function.;In the fourth and last part of the dissertation, we proposed a new massive gravity theory that is free of the vDVZ discontinuity. The key to the absence of the discontinuity is to introduce an extra scalar field with negative kinetic sign.