Primordial supersymmetric inflation

We discuss the motivations for reconsidering cosmological inflation in supersymmetric theories as contrasted with conventional GUTs. Radiative corrections to the effective potential can be made arbitrarily small in supersymmetric GUTs, removing some of the obstacles to inflation. We analyze general renormalizable potentials at the tree level and show that the required fine-tuning of parameters becomes less acute if inflation takes place before the grand unified phase transition, a hypothesis we term primordial inflation. We show how the grand unified monopole problem can be solved in supersymmetric GUTs embodying primordial inflation.     

No-scale supersymmetric GUTs

We construct locally supersymmetric GUTs in which radiative corrections determine all the mass scales which are hierarchically smaller than the Planck mass: $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{=}\text{O}\text{(m}{}_{\mathrm{<mtext>W</mtext>}}\text{) =}\text{exp}\text{(}\text{?}\text{O}\text{(1)}\text{α}{}_{\mathrm{<mtext>t</mtext>}}\text{)m}{}_{\mathrm{<mtext>p</mtext>}}$, etc. Such no-scale GUTs are based on a hidden sector with a flat potential guaranteed by SU(1, 1) conformal invariance. This is extended to include observable chiral fields in an SU(n, 1)/SU(n) × U(1) structure reminiscent of N ? 5 extended supergravity theories. Tree-level supersymmetry breaking is present only for the gravitino, and for the light gaugino masses through non-minimal kinetic terms reminiscent of N?4 extended supergravity theories. Radiative corrections generate squark and slepton masses which are phenomenologically acceptable, and the right value of m_W is obtained if m_t ≈ 50 GeV in the simplest such model.     

A supersymmetric gut

We propose a grand unified supersymmetric theory based on SU(5) with spontaneously broken supersymmetry. The theory (really a class of theories) is completely realistic. In particular, supersymmetry partners of ordinary fermions and bosons are heavy. The model requires one fine-tuning in order to render the color triplet partners of the Higgs fields (which mediate proton decay) superheavy. This fine-tuning is stable against radiative corrections. At the tree level, the model contains two scales, the unification scale, of order 10¹⁶ GeV, and the supersymmetry breaking scale, of order 10¹⁰ GeV. The breaking of SU(2) × U(1) invariance arises as a radiative effect. The lightest of the new particles implied by supersymmetry are expected to have masses of order tens of GeV.     

Successful supersymmetric inflation

We reconsider the problems of cosmological inflation in effective supergravity theories. A singlet field in a hidden sector is demonstrated to yield an acceptable inflationary potential, without fine tuning. In the simplest such model, the requirement of generating the microwave background anisotropy measured by COBE fixes the inflationary scale to be about 10¹⁴ GeV, implying a reheat temperature of order 10⁵ GeV. This is low enough to solve gravitino problem but high enough to allow baryogenesis after inflation. Such consistency requires that the generation of gravitational waves be negligible and that the spectrum of scalar density perturbations depart significantly from scale invariance, thus improving the fit to large-scale structure in an universe dominated by cold dark matter. We also consider the problems associated with gravitino production through inflaton decay and with other weakly coupled fields such as the moduli encountered in (compactified) string theories.     

Minimal supersymmetric technicolor

We introduce novel extensions of the Standard Model featuring a supersymmetric technicolor sector. First we consider N=4\mathcal{N}=4 Super Yang–Mills which breaks to N=1\mathcal{N}=1 via the electroweak (EW) interactions and coupling to the MSSM. This is a well defined, economical and calculable extension of the SM involving the smallest number of fields. It constitutes an explicit example of a natural supersymmetric conformal extension of the Standard Model featuring a well defined connection to string theory. It allows us to interpolate, depending on how we break the underlying supersymmetry, between unparticle physics and Minimal Walking Technicolor. As a second alternative we consider other N = 1\mathcal{N} =1 extensions of the Minimal Walking Technicolor model. The new models allow all the standard model matter fields to acquire a mass.     

More supersymmetric technicolor

We propose a supersymmetric model of particle physics in which supersymmetry is broken by strong gauge forces. Unlike previous realistic supersymmetric technicolor theories, the model contains only one extra strong gauge group, and it lends itself readily to grand unification. The model also has no light axions which can burn out stars. A variety of new particles, many weighing less than 100 GeV, are predicted. A no-go theorem due to Witten is discussed.     

Possible supersymmetric kinematics

The contraction method in different limits to obtain 22 different realizations of kinematical algebras is applied to study the supersymmetric extension of Ad S algebra and its contractions. It is shown that p2 h-, p, c2 and g algebras, in addition to d-, p, n-, g and c algebras, have supersymmetric extension, while n-2, g2 and g 2algebras have no supersymmetric extension. The connections among the superalgebras are established.     

Deformed supersymmetric oscillators

We construct and discuss the Fock-space representation and the number operator for a deformed supersymmetric oscillator with “peculiar” statistics. We suggest a possible generalization to multimode deformed oscillators.     

A supersymmetric Sawada-Kotera equation

A new supersymmetric equation is proposed for the Sawada-Kotera equation. The integrability of this equation is shown by the existence of Lax representation and infinite conserved quantities and a recursion operator.     

Naturalnes in supersymmetric GUTS

We propose a resummation of QCD radiative corrections in large transverse momentum hadronic processes, based on the introduction of an infrared cut-off, linked to the confinement radius. An analysis of the inclusive reactionspp → π⁰ X andpp → γX and of γ/π⁰ ratio is presented.     

PT-symmetrized supersymmetric quantum mechanics

Supersymmetry between bosons and fermions is modelled withinPT-symmetric quantum mechanics. A non-Hermitian alternative to the Witten’s supersymmetric quantum mechanics is obtained. Work supported by the grant Nr. A 1048004 of GA AS CR. Presented at the DI-CRM Workshop held in Prague, 18–21 June 2000.     

A supersymmetric anharmonic oscillator

We consider the supersymmetric model obtained from the Wess-Zumino model with interaction, with the help of a dimensional reduction. The solution is found of the corresponding classical problem with a precision up to terms of the third order of smallness. A quantum model of such a system is constructed. Its spectrum is found in the first and second order of perturbation theory. The supersymmetric finite-dimensional model under consideration proves to be extremely close to the usual anharmonic oscillator.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 28–32, May, 1990.     

Towards supersymmetric subconstituent models

't Hooft's consistency equations for subconstituent models are generalized to supersymmetric theories and a few solutions are outlined.     

No-scale supersymmetric standard model

We propose a class of supergravity models coupled to matter in which the scales of supersymmetry breaking and of weak gauge symmetry breaking are both fixed by dimensional transmutation, not put in by hand. The models have a flat potential with zero cosmological constant before the evaluation of weak radiative corrections which determine $\text{m}\text{3}\text{2}\text{, m}{}_{\mathrm{<mtext>W</mtext>}}\text{=}\text{exp}\text{[}\text{?O(1)}\text{α}{}_{\mathrm{<mtext>t</mtext>}}\text{]m}{}_{\mathrm{<mtext>p</mtext>}}\text{:α}{}_{\mathrm{<mtext>t</mtext>}}\text{= O(α)}$. These models are consistent with all particle physi cs and cosmological constraints for top quark masses in the range 30 GeV < m_t < 100 GeV.     

Decoupling of supersymmetric particles

The possibility of a heavy supersymmetric spectrum at the Minimal Supersymmetric Standard Model is considered and the decoupling from the low energy electroweak scale is analyzed in detail. The formal proof of decoupling of supersymmetric particles from low energy physics is stated in terms of the effective action for the particles of the Standard Model that results by integrating out all the sparticles in the limit where their masses are larger than the electroweak scale. The computation of the effective action for the standard electroweak gauge bosons , Z and is performed by integrating out all the squarks, sleptons, charginos and neutralinos to one-loop. The Higgs sector is not considered in this paper. The large sparticle masses limit is also analyzed in detail. Explicit analytical formulae for the two-point functions of the electroweak gauge bosons to be valid in that limit are presented. Finally, the decoupling of sparticles in the S, T and U parameters is studied analitically. A discussion on how the decoupling takes place in terms of both the physical sparticle masses and the non-physical mass parameters as the -parameter and the soft-breaking parameters is included. Received: 27 March 1998 / Published online: 5 October 1998     

Detection of supersymmetric signals

A discussion is given of a new method to isolate supersymmetric signals. As the presence of missing mass in the supersymmetric reactions is one of the biggest problems, the principal advantage of the new method proposed is its ability to offer an estimate of the mass of the produced superpartners. The technique has been successfully applied to the HERA environment, where errors of 10% on the mass values have been obtained, even starting from very few detected events.     

Non-commutative supersymmetric quantum mechanics

General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two- and three-dimensional examples are explicitly studied. The structure of the theory studied suggest other possible applications in physical systems with potentials involving spin and non-local interactions.