In this paper, we present a new scenario of the early Universe that contains a pre big bang Ekpyrotic phase. By combining this with a ghost condensate, the theory explicitly violates the null energy condition without developing any ghost-like instabilities. Thus the contracting universe goes through a non-singular bounce and evolves smoothly into the expanding post big bang phase. The curvature perturbation acquires a scaleinvariant spectrum well before the bounce in this scenario. It is sourced by the scaleinvariant entropy perturbation engendered by two ekpyrotic scalar fields, a mechanism recently proposed by Lehners et al. Since the background geometry is non-singular at all times, the curvature perturbation remains nearly constant on super horizon scales. It emerges from the bounce unscathed and imprints a scale-invariant spectrum of density fluctuations in the matter-radiation fluid at the onset of the hot big bang phase. The ekpyrotic potential can be chosen so that the spectrum has a "red" tilt, in accordance with the recent data from WMAP. As in the original Ekpyrotic scenario, the model predicts a negligible gravity wave signal on all observable scales. As such "New Ekpyrotic Cosmology" provides a consistent and distinguishable alternative to inflation to account for the origin of the seeds of large scale structure.

One-loop amplitudes of gluons in supersymmetric Yang-Mills are four-dimensional cut-constructible. This means that they can be determined from their unitarity cuts.We present a new systematic procedure to explicitly carry out any finite unitarity cut integral. The procedure naturally separates the contributions from bubble, triangle and box scalar integrals. This technique allows the systematic calculation of N = 1 amplitudes of gluons. As an application we compute all next-to-MHV six-gluon amplitudes in N = 1 super-Yang-Mills.

The background field method for N = 2 super Yang-Mills theories in harmonic superspace is developed. The ghost structure of the theory is investigated. It is shown that the ghosts include two fermionic real ω-hypermultiplets (FaddeevPopov ghosts) and one bosonic real ω-hypermultiplet (Nielsen-Kallosh ghost), all in the adjoint representation of the gauge group. The one-loop effective action is analysed in detail and it is found that its structure is determined only by the ghost corrections in the pure super Yang-Mills theory. As applied to the case of N = 4 super Yang-Mills theory, realized in terms of N = 2 superfields, the latter result leads to the remarkable conclusion that the one-loop effective action of the theory does not contain quantum corrections depending on the N = 2 gauge superfield only. We show that the leading low-energy contribution to the one-loop effective action in the N = 2 SU (2) super Yang-Mills theory coincides with Seiberg's perturbative holomorphic effective action.

The problem of the stabilization of moduli is discussed within the context of compactified strongly coupled heterotic string theory. It is shown that all geometric, vector bundle and five-brane moduli are completely fixed, within a phenomenologically acceptable range, by non-perturbative physics. This result requires, in addition to the full space of moduli, non-vanishing Neveu-Schwarz flux, gaugino condensation with threshold corrections and the explicit form of the Pfaffians in string instanton superpotentials. The stable vacuum presented here has a negative cosmological constant. The possibility of "lifting" this to a metastable vacuum with positive cosmological constant is briefly discussed.