Gauge Coupling Constant Unification With Planck Scale Values Of Moduli

Convergence of the standard model gauge coupling constants to a common value at around $2\times 10^{16}$ GeV is studied in the context of orbifold theories where the modular symmetry groups for $T$ and $U$ moduli are broken to subgroups of $PSL(2, Z)$. The values of the moduli required for this unification of coupling constants are studied for this case and also for the case where string unification is accompanied by unification to a gauge group larger then $SU(3)\times SU(2)\times U(1).$Comment: Tex, 15 pages, minor typos corrected and some references adde

CP-violating phases in the CKM matrix in orbifold compactifications

The picture of CP-violation in orbifold compactifications in which the $T$-modulus is at a complex fixed point of the modular group is studied. CP-violation in the neutral kaon system and in the neutron electric dipole moment are both discussed. The situation where the $T$-modulus takes complex values on the unit circle which are not at a fixed point is also discussed.Comment: LaTeX file 17 page

Magnetic Interactions, the Renormalization Group and Color Superconductivity in High Density QCD

We investigate the effect of long range magnetic interactions on the renormalization group (RG) evolution of local Cooper pairing interactions near the Fermi surface in high density QCD. We use an explicit cut-off on momentum modes, with special emphasis on screening effects such as Landau damping, to derive the RG equations in a gauge invariant, weak coupling expansion. We obtain the Landau pole $\Delta \sim \mu g^{-5} \exp(- \frac{3 \pi^2}{\sqrt{2} g})$, although the structure of our equations differs from previous results. We also investigate the gap equation, including condensates of higher angular momentum. We show that rotational invariance is unbroken at asymptotically high density, and verify that $\Delta$ is the correct value of the gap when higher modes are included in the analysis.Comment: 17 pages, 3 figures, late

A Model for Clumpy Self-Enrichment in Globular Clusters

Detailed observations of globular clusters (GCs) have revealed evidence of self-enrichment: some of the heavy elements that we see in stars today were produced by cluster stars themselves. Moreover, GCs have internal subpopulations with different elemental abundances, including, in some cases, in elements such as iron that are produced by supernovae. This paper presents a theoretical model for GC formation motivated by observations of Milky Way star forming regions and simulations of star formation, where giant molecular clouds fragment into multiple clumps which undergo star formation at slightly different times. Core collapse supernovae from earlier-forming clumps can enrich later-forming clumps to the degree that the ejecta can be retained within the gravitational potential well, resulting in subpopulations with different total metallicities once the clumps merge to form the final cluster. The model matches the mass-metallicity relation seen in GC populations around massive elliptical galaxies, and predicts metallicity spreads within clusters in excellent agreement with those seen in Milky Way GCs, even for those whose internal abundance spreads are so large that their entire identity as a GC is in question. The internal metallicity spread serves as an excellent measurement of how much self-enrichment has occurred in a cluster, a result that is very robust to variation in the model parameters.Comment: ApJ, in press. 18 pages. Code instantiating the model is at doi:10.5281/zenodo.125334

The KM phase in semi-realistic heterotic orbifold models

In string-inspired semi-realistic heterotic orbifolds models with an anomalous $U(1)_X$, a nonzero Kobayashi-Masakawa (KM) phase is shown to arise generically from the expectation values of complex scalar fields, which appear in nonrenormalizable quark mass couplings. Modular covariant nonrenormalizable superpotential couplings are constructed. A toy $Z_3$ orbifold model is analyzed in some detail. Modular symmetries and orbifold selection rules are taken into account and do not lead to a cancellation of the KM phase. We also discuss attempts to obtain the KM phase solely from renormalizable interactions.Comment: Error in Section 2, "Counterexamples," correcte

Stabilising the supersymmetric Standard Model on the Z_6' orientifold

Four stacks of intersecting supersymmetric fractional D6-branes on the Z_6' orientifold have previously been used to construct consistent models having the spectrum of the supersymmetric Standard Model, including a single pair of Higgs doublets, plus three right-chiral neutrino singlets. However, various moduli, Kahler moduli and complex-structure moduli, twisted and untwisted, remain unfixed. Further, some of the Yukawa couplings needed to generated quark and lepton masses are forbidden by a residual global symmetry of the model. In this paper we study the stabilisation of moduli using background fluxes, and show that the moduli may be stabilised within the Kahler cone. In principle, missing Yukawa couplings may be restored, albeit with a coupling that is suppressed by non-perturbative effects, by the use Euclidean D2-branes that are pointlike in spacetime, i.e. E2-instantons. However, for the models under investigation, we show that this is not possible.Comment: 32 pages, LaTeX. Small addition made prior to submission for publicatio

Modular Symmetries of Threshold Corrections for Abelian Orbifolds with Discrete Wilson Lines

The modular symmetries of string loop threshold corrections for gauge coupling constants are studied in the presence of discrete Wilson lines for all examples of abelian orbifolds, where the point group is realised by the action of Coxeter elements or generalised Coxeter elements on the root lattices of the Lie groups.Comment: 36 pages, Late

Almost the supersymmetric Standard Model from intersecting D6-branes on the Z_6' orientifold

Intersecting stacks of supersymmetric fractional branes on the Z_6' orientifold may be used to construct the supersymmetric Standard Model. If a,b are the stacks that generate the SU(3)_{colour} and SU(2)_L gauge particles, then, in order to obtain {\em just} the chiral spectrum of the (supersymmetric) Standard Model (with non-zero Yukawa couplings to the Higgs mutiplets), it is necessary that the number of intersections a \cap b of the stacks a and b, and the number of intersections a \cap b' of a with the orientifold image b' of b satisfy (a \cap b,a \cap b')=(2,1) or (1,2). It is also necessary that there is no matter in symmetric representations of the gauge group, and not too much matter in antisymmetric representations, on either stack. Fractional branes having all of these properties may be constructed on the Z_6' orientifold. We construct a (four-stack) model with two further stacks, each with just a single brane, which has precisely the matter spectrum of the supersymmetric Standard Model, including a single pair of Higgs doublets. However, the gauge group is SU(3)_{\rm colour} x SU(2)_L x U(1)_Y x U(1)_H. Only the Higgs doublets are charged with respect to U(1)_H.Comment: 8 pages, no figure