Particle theory

Abstract:

Theories with non-Abelian flavour symmetries lead at zeroth order to neutrino degeneracy and massless charged fermions. The flavour symmetry is spontaneously broken sequentially to give hierarchies $\Delta m_{atm}^2 \gg \Delta m_{\odot}^2$ and $m_\tau \gg m_\mu \gg m_e$, and a misalignment of the vacuum between neutrino and charged sectors gives large $\theta_{atm}$. Explicit models are given which determine $\theta_{atm} = 45^\circ$. A similar construction gives vacuum misalignment for the lighter generations and gives a vanishing $\beta \beta_{0 \nu}$ rate, so that there is no laboratory constraint on the amount of neutrino hot dark matter in the universe, and the solar mixing angle is also maximal, $\theta_\odot = 45^\circ$.

Abstract:

We calculate the spectral density of the Dirac operator over an ensemble of configurations composed of overlapping instantons and anti-instantons. We find evidence that the spectral density diverges in the limit λ → 0. This indicates the breaking of chiral symmetry and also provides evidence that quenched QCD may be pathological in nature.

Abstract:

Supersymmetry breaking via gaugino condensation is studied in vacua of heterotic M-theory with five-branes. We show that supersymmetry is still broken by a global mechanism and that the non-perturbative superpotential takes the standard form. When expressed in terms of low energy fields, a modification arises due to a threshold correction in the gauge kinetic function that depends on five-brane moduli. We also determine the form of the low energy matter field Kahler potential. These results are used to discuss the soft supersymmetry breaking parameters, in particular the question of universality.

Abstract:

We review the spectral cover formalism for constructing both U(n) and SU(n) holomorphic vector bundles on elliptically fibered Calabi-Yau three-folds which admit a section. We discuss the allowed bases of these three-folds and show that physical constraints eliminate Enriques surfaces from consideration. Relevant properties of the remaining del Pezzo and Hirzebruch surfaces are presented. Restricting the structure group to SU(n), we derive, in detail, a set of rules for the construction of three-family particle physics theories with phenomenologically relevant gauge groups. We show that anomaly cancellation generically requires the existence of non-perturbative vacua containing five-branes. We illustrate these ideas by constructing four explicit three-family non-perturbative vacua.