High Temperature Symmetry Nonrestoration

This is a short review on the subject of symmetry nonrestoration at high temperature. Special emphasis is put on experimental discoveries and different theoretical mechanisms. At the end, possible cosmological applications are briefly mentioned.Comment: 7 pages; plenary talk at COSMO99, Trieste, Italy, Sep 27 - Oct 2, 1999; to appear in the proceedings; minor text changes and new references adde

Do internal symmetries get restored in hot and dense SUSY?

I offer some computational details and useful and concise formulae to calculate the effective potential for a general abelian supersymmetric model at high temperature and density. It will be shown that such cases are very good candidates for symmetry nonrestoration at high temperature, providing large densities are present.Comment: 3 pages, uses sprocl.sty, talk given at the International Workshop COSMO97 on Particle Physics and the Early Universe, 15-19 September 1997, Ambleside, Lake District, England, to be published in the Proceeding

Proton decay, supersymmetry breaking and its mediation

We study the breaking of supersymmetry and its transmission to the light states in the context of the minimal SU(5) grand unified theory, with no additional singlets. This simple theory can be taken as a prototype for a program of breaking simultaneously grand unified symmetry and supersymmetry. The main predictions are: (i) d=6 proton decay is completely negligible and d=5 is in accord with experiment, (ii) supersymmetry breaking is mainly mediated by gravity.Comment: 18 page

Towards the minimal renormalizable supersymmetric E6E_6 model

We find an explicit renormalizable supersymmetric $E_6$ model with all the ingredients for being realistic. It consists of the Higgs sector $351'+\overline{351'}+27+\overline{27}$, which breaks $E_6$ directly to the Standard Model gauge group. Three copies of $27$ dimensional representations then describe the matter sector, while an extra $27+\overline{27}$ pair is needed to successfully split the Standard Model Higgs doublet from the heavy Higgs triplet. We perform the analysis of the vacuum structure and the Yukawa sector of this model, as well as compute contributions to proton decay. Also, we show why some other simpler $E_6$ models fail to be realistic at the renormalizable level.Comment: 36 pages, a new section on proton decay added, new reference, results unchanged. To be published in JHE

Hidden flavor symmetries of SO(10) GUT

The Yukawa interactions of the SO(10) GUT with fermions in 16-plets (as well as with singlets) have certain intrinsic ("built-in") symmetries which do not depend on the model parameters. Thus, the symmetric Yukawa interactions of the 10 and 126 dimensional Higgses have intrinsic discrete $Z_2\times Z_2$ symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional Higgs have a continuous SU(2) symmetry. The couplings of SO(10) singlet fermions with fermionic 16-plets have $U(1)^3$ symmetry. We consider a possibility that some elements of these intrinsic symmetries are the residual symmetries, which originate from the (spontaneous) breaking of a larger symmetry group $G_f$. Such an embedding leads to the determination of certain elements of the relative mixing matrix $U$ between the matrices of Yukawa couplings $Y_{10}$, $Y_{126}$, $Y_{120}$, and consequently, to restrictions of masses and mixings of quarks and leptons. We explore the consequences of such embedding using the symmetry group conditions. We show how unitarity emerges from group properties and obtain the conditions it imposes on the parameters of embedding. We find that in some cases the predicted values of elements of $U$ are compatible with the existing data fits. In the supersymmetric version of SO(10) such results are renormalization group invariant.Comment: 28 pages, a reference added, typos corrected, to be published in NP

On the matching method and the Goldstone theorem in holography

We study the transition of a scalar field in a fixed $AdS_{d+1}$ background between an extremum and a minimum of a potential. We compute analytically the solution to the perturbation equation for the vev deformation case by generalizing the usual matching method to higher orders and find the propagator of the boundary theory operator defined through the AdS-CFT correspondence. We show that, contrary to what happens at the leading order of the matching method, the next-to-leading order presents a simple pole at $q^2=0$ in accordance with the Goldstone theorem applied to a spontaneously broken dilatation invariance.Comment: 16 pages, 1 figure, published versio