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.     

Impossibility of adding gauge couplings to spontaneously broken N = 8 supergravity

When the four mass parameters of spontaneously broken N = 8 supergravity are taken to be equal, the theory possesses at global SU(4) symmetry. Since it contains massless vectors in the adjoint representation, it is tempting to add gauge interactions so as to make the SU(4) symmetry local. In this paper we show that it is impossible to do this in a way that is consistent with the spontaneous character of the symmetry breaking.     

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.     

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.     

Formation time of F centers in alkali halides

It is argued that in most alkali halides an appreciable fraction of the self-trapped excitons may undergo non-radiative transitions from vibrationally excited states of B_3u to the A_1g state during the relaxation of the self-trapped excitons created by ionizing radiation. Numerical calculations show that the non-radiative transition probabilities, from vibrational levels of B_3u near or above the crossing point of the A_1g and B_3u potential curves to the A_1g state, are consistent with the observed formation times of F centers in various alkali halides. The exceptional case of KI is also discussed.     

Spontaneous supersymmetry breaking by large-N matrices

Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity. In our models, the large value of N gives a natural explanation for the origin of small parameters appearing in the field theories which trigger the supersymmetry breaking.     

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.     

Fourier transform emission spectroscopy of the FΔ-XΦ system of TiF

The emission spectra of TiF have been reinvestigated in the 4200-15 000 cm⁻¹ region using the Fourier transform spectrometer associated with the National Solar Observatory at Kitt Peak. TiF was formed in a microwave discharge lamp operated with 2.5 Torr of He and a trace of TiF₄ vapor, and the spectra were recorded at a resolution of 0.02 cm⁻¹. The TiF bands observed in the 12 000-14 000 cm⁻¹ region have been assigned to a new transition, F⁴Δ-X⁴Φ. Each band consists of four sub-bands assigned as, ⁴Δ_1/2-⁴Φ_3/2, ⁴Δ_3/2-⁴Φ_5/2, ⁴Δ_5/2-⁴Φ_7/2, and ⁴Δ_7/2-⁴Φ_9/2. A rotational analysis of the 0-1, 0-0, and 1-0 bands has been obtained and spectroscopic constants have been extracted.     

Representations of N = 4 supersymmetry on superfields

We determine all of the irreducible representations (irreps) of the extended supersymmetry algebra (for N = 2 and 4) on superfields with arbitrary external spin in terms of the associated eigenvalues of suitable Casimirs of enlarged algebras. Detailed results are presented for the scalar, spinor and vector superfield cases. The component content of the corresponding irreps are also discussed by means of suitable basis functions.     

Finiteness, 1/N expansion and supersymmetry breaking

The possibility of spontaneous supersymmetry breaking in the limit of large N, in models with an internal O(N) symmetry, is demonstrated by constructing an explicit example in two dimensions. The model is finite and this is shown to be important for the supersymmetry breaking. A general criterion for finiteness of scalar superfield theories in two dimensions is given. Finally, the generalization of our results to three dimensions, and their relevance to four-dimensional models, is discussed.     

On the luminescence quenching of F centres in alkali halides

Non-radiative transitions from the excited state of F center to the ground state occur very efficiently around and above, over a rather large interval of energy, the crossing point of the two adiabatic potential energy curves. Taking this effect into account the criterion for luminescence quenching originally proposed by Dexter et al. is re-examined. The luminescence quantum efficiency is estimated for those alkali halides in which the luminescence is weak, and the results are in general accord with experiment. The border-line case of NaCl is also explained.     

Compactification and supersymmetry in d = 11 supergravity

We examine the conditions under which the ground state of d = 11 supergravity can be supersymmetric and be of the form M⁴ ? B⁷ with M⁴ Minkowski spacetime and B⁷ a compact seven-dimensional manifold. Since we have in mind a background that renders the effective action stationary we make no use of the classical field equations. We find that the requirement that the four-space be flat is very restrictive. It requires all components of the background four-index field to vanish and the compact manifold to be Ricci-flat and hence to have at most the abelian symmetries associated with tori.     

Off-shell N = 8 supersymmetry with central charges

Using a new technique of dimensional reduction by Legendre transformation we derive an off-shell formulation of the N = 8 extended supersymmetry algebra, which is realised in the maximally extended supergravity theory. The theory has an Sp(8) manifest global invariance and some of the fields satisfy differential constraints.     

Ultraviolet behaviour of spontaneously broken gauge theories

The asymptotic invariant coupling constant (ICC) in the repulsive σ⁴ interaction is shown to be finite in the second logarithmic approximation. It leads to spontaneously broken gauge theories free of ultraviolet (UV) troubles.     

Electron-lattice coupling of F centers: Particular case of NaI: F

Absorption and magnetic circular dichroism studies of the F centers in NaI reveal a strong electron-lattice coupling with the vibration modes of Γ₁⁺ symmetry in comparison with those of Γ₃⁺ and Γ₅⁺ symmetry. On the other hand, the F electron exhibits in its first excited state a large spin-orbit coupling, in agreement with the value previously calculated. These results are confirmed by the Raman spectra which show a predominant intensity for the Γ₁⁺ modes, particularly for the resonant mode at 113 cm^?1.First and second-order Raman spectra have been calculated using a “quasi-resonant” theory in which the vibrations of the ions up to the fifth shell have been taken into consideration. We have been able to determine from these calculations absolute values for the contributions of the different types of vibration modes to the broadening of the F-absorption band.     

A spontaneously broken conformal gauge theory of gravitation

In a fusing of a few attractive ingredients, we consider a spontaneously broken conformal gauge theory of gravitation, with an underlying Riemann-Cartan-Weyl geometry. The theory contains no intrinsic dimensional parameters, is unitary, and has the Schwarzschild metric as the unique spherically symmetric solution of the vacuum field equation (thus guaranteeing agreement with observed gravitational phenomena). The particle content of the theory consists of a massless 2^. graviton, and a super-massive 1^? “conformon”.