Astrophysical constraints on broken supersymmetry

Arguments on the evolution of stars at an advanced stage constrain the interaction strength of light neutral fermions appearing in broken supersymmetric theories. In particular a consideration of white dwarfs leads to a bound on the fundamental scale of supersymmetry breaking d > 2.6 × 10³GeV², an order of magnitude improvement compared to the existing bound. A new bound on the scalar electron mass is obtained also.     

Algebraic structure of broken supersymmetry

The algebraic structure of a certain class of broken supersymmetry theories is found to be quite similar to that of Yang-Mills theories spontaneously broken by a Higgs mechanism. Certain peculiar features arising in the case of broken supersymmetry can be traced to the field dependence of the local gauge algebra.     

Parity conservation in broken supersymmetry theories

It is pointed out that the supersymmetry breaking technique introduced by Slavnov and Fayet can be applied to parity conserving models, and an example of such a model is given     

Partially broken global supersymmetry and the superstring

We study the partial spontaneous breaking of a global supersymmetry algebra. A formalism developed by Volkov for nonlinearly realized spacetime symmetries is very useful. The case analyzed in detail is two-dimensional (2,2) supersymmetry with a central charge spontaneously broken to (0,2). This algebra, which is realized in supersymmetric Nielsen-Olesen strings, leads to the Green-Schwarz superstring action.     

Softly broken supersymmetry and the fine-tuning problem

The supersymmetry of the simple Wess-Zumino model is broken, in the tree-approximation, by adding all possible parity-even [mass]-dimension 2 and 3 terms. The model is then renormalized using BPHZ and the normal product algorithm, such that supersymmetry is only softly broken (in the original sense of Schroer and Symanzik).We show that, within the above renormalization scheme, none of the added breaking terms give rise to technical fine-tuning problems (defined in the sense of Gildener) in larger models, with scalar multiplets and hierarchy of mass scales, which is in contrast to what we obtain via analytic schemes such as dimensional renormalization, or supersymmetry extension of which.The discrepancy (which can be shown to persist in more general models) originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Emphasizing that the issue is purely technical (as opposed to physical) in origin, and that all physical properties are scheme-independent (as they should be!), we conclude that the technical fine-tuning problem, in the specific sense used in this paper, being scheme dependent, is not a well-defined issue within the context of renormalized perturbation theory.     

Superfield propagators and supergraphs for broken supersymmetry

A method to calculate superfield propagators for models with explicitly soft or spontaneously broken supersymmetry is presented. The Feynman rules for this case are shown to be slightly modified compared to the symmetric case. The method is also applied to an effective potential calculation.     

Analytical constraints in extended supersymmetry

Starting from the deep relation between the system of numbers and extended supersymmetry we can obtain analytical constraints for superfields.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

Fluctuations in nonequilibrium systems and broken supersymmetry

The fluctuation-dissipation theorem is not expected to hold for systems that either violate detailed balance or have time-dependent or nonpotential forces. Therefore the relation between response and correlation functions should have contributions due to the nonequilibrium nature. An explicit formula for such a contribution is calculated, which in the present derivation appears as a historydependent term. These relations are the Ward-Takahashi identities of a supersymmetric formulation of the Langevin models, and the new term results from a broken supersymmetry.     

Structure of phenomenological lagrangians for broken supersymmetry

We consider the explicit connection between linear representations of supersymmetry and the non-linear realizations associated with the generic effective lagrangians of the Volkov-Akulov type. We specify and illustrate a systematic approach for deriving the appropriate phenomenological lagrangian by transforming a pedagogical linear model, in which supersymmetry is broken at the tree level, into its corresponding non-linear lagrangian, in close analogy to the linear σ model of pion dynamics. We discuss the significance and some properties of such phenomenological lagrangians.     

Softly broken supersymmetry and SU(5)

We construct an explicit realistic SU(5) model in which softly broken supersymmetry is used to protect the Higgs doublets from quadratic mass renormalization. The model requires one natural but incredibly accurate adjustment of parameters. We argue that such an adjustment will be required in any supersymmetric GUT in which baryon number is not conserved.     

Softly broken supersymmetry and radiative gauge symmetry breaking

We compare two approaches to quantum corrections in theories with softly broken supersymmetry: the effective potential à la Coleman-Weinberg and the scaling of parameters of the tree level potential between M_PL and M_W, which has been used recently in the context of low-energy supergravity in order to obtain radiative SU(2) × U(1) symmetry breaking. Corrections to the latter procedure are studied in simple models and estimated in the general case.     

Mass formula for pseudo-goldstone fermions in broken supersymmetry

The goldstino of spontaneously broken supersymmetry develops a mass in the presence of perturbations which violate supersymmetry explicitly. In analogy to the chiral dynamics of pions, the general current algebra formula for this mass is derived. It is verified and illustrated in simple models at the tree level or through loop expansions. Some subtleties of the renormalization and the vacuum stability of the relevant O'Raifeartaigh-type models are examined.     

The spontaneously broken supersymmetry in quantum field theory

It is shown that every spontaneous breaking of supersymmetry can be accomplished by means of a locally conserved supercurrent

$\text{εαβf}{}^{\mathrm{+}}{}_{\mathrm{<mtext>\gamma </mtext><mtext>?</mtext>}}\text{, α, β, γ = 1, 2,}$

$\text{εαβ =}\text{0}\text{1}\text{?1}\text{1}$

, where $\text{f}{}^{\mathrm{+}}{}_{\mathrm{<mtext>\gamma </mtext><mtext>?</mtext>}}$ is a massless field satisfying the Weyl Equation. For a given supercurrent $\text{jαβ}\text{γ}\text{?}$ the necessary condition that it will break spontaneously the supersymmetry is

$\text{jαβ}\text{γ}\text{?}\text{?jβα}\text{γ}\text{?}\text{≠0.}$

It is shown that the anticommutation relations of the broken supercharges are not related to the energy-momentum vector.Similar procedure applied in case of a vector field is inconclusive.The extension of the Maisson and Reeh statement on the helicity of Goldstone fields is given.     

The broken supersymmetry phase of a self-avoiding random walk

We consider a weakly self-avoiding random walk on a hierarchical lattice ind=4 dimensions. We show that for choices of the killing ratea less than the critical valuea _cthe dominant walks fill space, which corresponds to a spontaneously broken supersymmetry phase. We identify the asymptotic density to which walks fill space, (a), to be a supersymmetric order parameter for this transition. We prove that (a)(a _c–a) (–log(a _c–a))^1/2 asaa _c, which is mean-field behavior with logarithmic corrections, as expected for a system in its upper critical dimension.Research partially supported by NSF Grants DMS 91-2096 and DMS 91-96161.     

A hamiltonian with broken supersymmetry for the xenon isotopes

A hamiltonian with broken $\text{u}\text{(}\text{6}\text{2}\text{j+1)}$ supersymmetry is proposed that can describe collective excitations in nuclei with high-spin, single-j orbitals. Its bosonic part is identical with IBA, while the fermionic degrees of freedom, are characterized by the seniority quantum number. The ground state as well as excited energies of eight xenon isotopes with both odd and even mass are fairly well described by the so(6) limit of this hamiltonian with only one set of parameters.     

Photon signatures for low energy supersymmetry breaking and broken R-parity

The possible phenomenological consequences of R-parity violating interactions in the framework of low energy supersymmetry breaking are studied. It is pointed out that even very weak R-parity violation would completely overshadow one of the basic signatures of low energy supersymmetry breaking models, that is the decay of the next to lightest supersymmetric particle into a photon (lepton) and missing energy. Thus, the observation of these decays would put very strong limits on R-parity violating couplings. Vice-versa, if R-parity violation is established experimentally, before a detailed knowledge of the spectrum is obtained, it will be very difficult to distinguish gravity mediated from low energy gauge mediated supersymmetry breaking scenarios. Those conclusions are very model independent. We also comment on the possibility of mixing between charged and neutral leptons with charginos and neutralinos, respectively, and its phenomenological consequences for the photon (lepton) signatures, in scenarios where this mixing is generated by the presence of bilinear or trilinear R-parity violating terms in the superpotential.