Natural suppression of proton decay in supersymmetric type III seesaw models

Supersymmetric Standard Model (MSSM) has two sources of rapid proton decay: (i) R-parity breaking terms and (ii) higher dimensional Planck induced B-violating terms; its extensions to include neutrino masses via the type I seesaw mechanism need not have the first of these problems due to the existence of B−L as a gauge symmetry but for sure always have the second one. If instead, neutrino masses are explained in a type III seesaw extension of standard model, an anomaly free gauge symmetry different from B−L is known to exist. In this note, it is shown that a realistic supersymmetric versions of this model can be constructed (MSSM as well as SUSY left–right with type III seesaw) which eliminate R-parity violating couplings and suppress Planck scale contributions to proton decay. The degree of suppression of the latter depends on the weak gauge group. For the left–right case, the suppression to the desired level is easily achieved.     

Supersymmetric inflation of dynamical origin

Dynamical models of inflation are given with composite inflatons by means of massive supersymmetric gauge theory. Nearly flat directions and stable massive ones in the potential are identified and slow-roll during inflation is examined. This kind of dynamical inflations may be ubiquitous in fundamental unified theory with supersymmetry, which should contain gauge theories for interactions of elementary particles.     

The origin of double inflation

Double inflation is a typical solution of fourth-order gravity, $$L_{grav} = M^2 R - R^2 /6$$ minimally coupled to a scalar field with mass m, and 0pl. For equipartition of initial conditions at the Planck era, being equivalent to the Gibbons-Hawking-Stewart measure, we get the probability of double inflation to be about $$p = 1 - mM/M_{pl}^2 $$ Fort → ∞ and a scalar field or ideal fluid as source, the solutions for the scale factor oscillate around a～t^2/3, thus theR ² term gives effectively dustthe dark matter of the universe. The big bang is generically ofa ～ t^1/2 type, independent of the matter. ForM=0 and radiation as source the exact solutiona(t)=[sinh(2H ₀ t)]^1/2 supports the attractor property of the de Sitter solution.     

Cold dark matter candidate in a class of supersymmetric models with an extra U(1)

In supersymmetric models whose gauge group includes an additional U(1) factor at the TeV scale, broken by the VEV of an standard model singlet S, the parameter space can accommodate a very light neutralino not ruled out experimentally. This higgsino-like fermion, stable if R-parity is conserved, can make a good cold dark matter candidate. We examine the thermal relic density of this particle and discuss the prospects for its direct detection if it forms part of our galactic halo.     

Matrix model in a class of time dependent supersymmetric backgrounds

We discuss the matrix model in a class of 11D time dependent supersymmetric backgrounds as obtained in [B. Chen, Phys. Lett. B 632 (2006) 393, hep-th/0508191]. We construct the matrix model action through the matrix regularization of the membrane action in the background. We show that the action is exact to all orders of fermionic coordinates. Furthermore we discuss the fuzzy sphere solutions in this background.     

The spectrum of a class of supersymmetric theories with false vacua

The spectrum of a supersymmetric quantum mechanics model, whose potential has a steep supersymmetric minimum and a broad non-supersymmetric minimum, is analyzed. With the exception of the supersymmetric ground state, the low-energy spectrum is found to be determined entirely by the non-supersymmetric well. The model is motivated by effective lagrangians proposed for supersymmetric QCD. It is speculated that in an equivalent field theory exhibiting a supersymmetric true vacuum and a non-supersymmetric false vacuum, the false vacuum can play an important rôle in the physics, and that the lowest energy excitations are extended field configurations involving a new mass scale.     

Ultra-violet finiteness of supersymmetric non-linear sigma models

It is shown that N = 4 supersymmetric non-linear sigma models in two spacetime dimensions are ultra-violet finite to all orders in perturbation theory.     

Ramond sector of the supersymmetric minimal models

A Coulomb gas representation for the Ramond sectors of the N = 1 supersymmetric models is constructed. The fusion rules and the 4-point functions for the Ramond fields are calculated explicitly by this method and used to describe the Z₂ odd sectors of the tricritical Ising model and of the critical Kosterlitz-Thouless XY model.     

Exact inhomogeneous models of cosmological inflation

Exact spherically symmetric solutions of the Einstein equations with quasi-vacuum source p = −ε are found in the form of spatially inhomogeneous Tolman metrics describing the inflationary stage of the evolution of the universe. Ul’yanov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 3–7, February, 1998.     

Finiteness of N = 4 supersymmetric sigma models

The two-dimensional supersymmetric K3 σ-model is not renormalized in all orders of perturbation theory.     

Cosmological models consistent with supersymmetric compactiflcation of superstring theories

The compactification of 10-dimensional supergravity, coupled to super Yang-Mills theory, to curved 4-dimensional spacetimes is investigated. The requirement of unbroken supersymmetry leads to a set of consistency conditions. These are fairly restrictive, but nevertheless permit some nontrivial solutions, including the Milne universe. More general time-dependent metrics are also not ruled out.     

Natural suppression of flavour-changing neutral currents in supersymmetric gauge theories

Induced flavour-changing neutral currents (FCNC) in supersymmetric unified theories are investigated both in models with the standard SU(2)_L × U(1) gauge symmetry and in models with an extra ?(1) gauge symmetry. Supersymmetric extension of the natural flavour conservation laws for neutral currents is obtained by adding a condition regarding the assumed type of supersymmetry breaking. This condition ensures no direct flavour-changing couplings of neutral gauge-Higgs fermions and at the same time is necessary and sufficient for the natural suppression of the induced FCNC. It is found that in the class of models satisfying the new condition the contribution of the scalar partners of quarks to the induced strangeness-changing neutral current is comparable to that of the quarks in $\text{K}{}_{\mathrm{L}}\text{→ π}\text{π}$, while it is negligibly small in K_L ? K_S mass difference.