New Solution to Doublet-Triplet Splitting Problem in SU(N) SUSY GUTs: Towards an Unification of Flavour

The missing VEV solution to the doublet-triplet splitting problem in general SU(N) SUSY GUTs is found. Remarkably enough, it requires a strict equality of numbers of the fundamental colours and flavours in SU(N) and for the even-order groups (N=2k) gives the predominant breaking channel $SU(N) \to SU(k-1)_c\otimes SU(k-1)_f\otimes SU(2)_w\otimes U(1)\otimes U(1)'$ in the parameter natural area. The flavour subsymmetry breaking owing to some generic string inspired extra symmetries of the Higgs superpotential appears not to affect markedly the basic adjoint vacuum configuration in the model. Thus the both salient features of SM just as an interplay between colours and flavours (or families for due assignment of quarks and leptons) so the doublet structure of the weak interactions could be properly understood and accommodated in the framework of the minimal SU(8) model. Among its predictions the most crucial one belongs to the existence on the TeV scale just three families of pseudo-Goldstone bosons and their superpartners 3(5+\bar 5) + SU(5)-singlets which noticeably improve the unification picture of MSSM.Comment: 13 pages, LaTe

Black holes and Higgs stability

We study the effect of primordial black holes on the classical rate of nucleation of AdS regions within the standard electroweak vacuum. We find that the energy barrier for transitions to the new vacuum, which characterizes the exponential suppression of the nucleation rate, can be reduced significantly in the black-hole background. A precise analysis is required in order to determine whether the the existence of primordial black holes is compatible with the form of the Higgs potential at high temperature or density in the Standard Model or its extensions.Comment: 27 pages, 10 figures, conclusions expanded, to appear in JCA

BPS solitons in Lifshitz field theories

Lorentz-invariant scalar field theories in d+1 dimensions with second-order derivative terms are unable to support static soliton solutions that are both finite in energy and stable for d>2, a result known as Derrick's theorem. Lifshitz theories, which introduce higher-order spatial derivatives, need not obey Derrick's theorem. We construct stable, finite-energy, static soliton solutions in Lifshitz scalar field theories in 3+1 dimensions with dynamical critical exponent z=2. We exhibit three generic types: non-topological point defects, topological point defects, and topological strings. We focus mainly on Lifshitz theories that are defined through a superpotential and admit BPS solutions. These kinds of theories are the bosonic sectors of supersymmetric theories derived from the stochastic dynamics of a scalar field theory in one higher dimension. If nature obeys a Lifshitz field theory in the ultraviolet, then the novel topological defects discussed here may exist as relics from the early universe. Their discovery would prove that standard field theory breaks down at short distance scales.Comment: 14 pages, 4 figures; v2: references added and the x-axis scale of each figure has been change

Horava Gravity and Gravitons at a Conformal Point

Recently Horava proposed a renormalizable gravity theory with higher derivatives by abandoning the Lorenz invariance in UV. Here, I study the Horava model at $\lambda=1/3$, where an anisotropic Weyl symmetry exists in the UV limit, in addition to the foliation-preserving diffeomorphism. By considering linear perturbations around Minkowski vacuum, I show that the scalar graviton mode is completely disappeared and only the usual tensor graviton modes remain in the physical spectrum. The existence of the UV conformal symmetry is unique to the theory with the detailed balance and it is quite probable that $\lambda=1/3$ be the UV fixed point. This situation is analogous to $\lambda=1$, which is Lorentz invariant in the IR limit and is believed to be the IR fixed point.Comment: Added comments and references, Accepted in GER

Quantum Cosmology Aspects Of D3 Branes and Tachyon Dynamics

We investigate aspects of quantum cosmology in relation to string cosmology systems that are described in terms of the Dirac-Born-Infeld action. Using the Silverstein-Tong model, we analyze the Wheeler-DeWitt equation for the rolling scalar and gravity as well for $R\times{S^3}$ universe, by obtaining the wave functions for all dynamical degrees of freedom of the system. We show, that in some cases one can construct a time dependent version of the Wheeler-DeWitt (WDW) equation for the moduli field $\phi$. We also explore in detail the minisuperspace description of the rolling tachyon when non-minimal gravity tachyon couplings are inserted into the tachyon action.Comment: 29 pages, 3 figures, REVTeX 4; v2 clarifications, comments and references added; v3 more typos corrected, additional comments on the minisuperspace description of unstable universes, version published in JHE