The off-shell infrared problem in N = 1 supersymmetric yang-mills theories (II). General massless models

We prove that in a general massless N = I SYM theory off-shell Green functions exist such that Green functions of gauge invariant operators are supersymmetrically covariant. The off-shell infrared problem present in the superfield treatment of these theories is thus shown to remain a gauge artefact. The N = 2, 4 pure SYM theories are covered by this result and thus exist as N = 1 SYM theories.     

A smooth massless limit for supersymmetric QCD

We analyse in detail the behaviour of supersymmetric QCD with a number of flavours M smaller than the number of colours N, for quark masses smaller than the dynamically generated scale Λ. In this regime, we find it useful to move from meson superfields to Nambu–Goldstone-like variables. In particular we work out the mass spectrum and the set of decay constants that specify the interactions of the low-energy theory. We explicitly check that masses and decay constants have a consistent behaviour under decoupling and that they satisfy current algebra requirements. Finally we speculate about the massless limit. For vanishing quark masses, and only in this case, the relation between mesons and Nambu–Goldstone variables becomes singular. When analysed in terms of the Nambu–Goldstone superfields, the massless limit exhibits a spontaneous breaking of the flavour symmetry, with massless Goldstone modes embedded in an M²-dimensional complex moduli space. The symmetry-breaking order parameter is formally infinite, but this has the only effect of turning off the interactions between the chiral superfields. The massive case, for masses smaller than Λ, can be thought of as a perturbation around the massless case, with corrections that can be systematically computed in the effective theory.     

B−L non-conserving proton decay in guts

It is shown that B?L non-conserving proton decay (p→e^?π⁺π⁺ etc.) is allowed through gauge boson mixing in both SO(10) and E(6) GUTs, but not in the SU(5) GUT. The lifetime for this decay mode is estimated.     

Symmetries of massless Dirac equations and supersymmetric quantum mechanics

It is shown how symmetries of Dirac equations can be used to obtain constants of motion for nonrelativistic supersymmetric quantum Hamiltonians. In particular, conserved supercharges are found for a spin-1/2 particle in the field of a dyon which yield under anticommutation the generalized Runge-Lenz symmetry of the system.This work is supported in part through funds provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Fonds FCAR of the Quebec Ministry of Education.     

Superfluidity in liquid 3He. Condensation in the L = 2 or L = 3 state

The possibility of superfluidity in liquid ³He is investigated, and the corresponding critical temperatures is estimated. In the calculations are used reaction-matrix elements calculated earlier by means of Brueckner theory. The results indicate D-state or F-state pairing. The largest transition is obtained for L = 3, i.e., superfluidity corresponding to the triplet F-state seems to be more likely than the singlet D-state pairing predicted earlier.     

Naturally massless Higgs doublets in supersymmetric SU(5)

We construct a supersymmetric SU(5) model characterized by: (a) naturally massless doublet Higgs superfields; (b) the natural appearance of “light” coloured triplet Higgses of mass of the order 10¹⁰ GeV, and study proton decay as well as the generation of cosmic baryon asymmetry. We find that an appropriate choice of Higgs sector renders dimension-five operators kinematically irrelevant for the stability of the proton. Proton decay proceeds through Higgs boson exchange in terms of dimension-six operators mainly to ${\overline{v}}_{\mu }{K}^{+},v^{+}{K}^0$.     

The gauge-invariant N=2 supersymmetric σ-model with general scalar potential

We construct the supersymmetric σ-model, in six dimensions, for an arbitrary hyper-Kähler manifold, and its minimal coupling to super-Yang-Mills theory. Non-trivial reduction to five or four dimensions yields the corresponding five- or four-dimensional N = 2 supersymmetric model with general scalar potential. We discuss briefly the coupling to supergravity in six dimensions and we give the on-shell supergravity torsion constraints.     

The baryon ladder of the U(6,6)-symmetry

An unified classification of the Baryons is made with the help of the so-called Baryon ladder of U(6,6). For this reason a complete set of commuting operators (introduced in a previous paper), including the squares of the spin and the isotopic spin, their third projections, the hypercharge, the Baryon number and so on, is used. Multiplets of a nontraditional type are obtained, which are in good agreement with the experimental situation. A Baryon mass operator is introduced; it is diagonal in the particles. With its help series of mass formulas are obtained for Baryons with spin-parity $\text{(}\text{1}\text{2}\text{)}{}^{\mathrm{+}}$, $\text{(}\text{3}\text{2}\text{)}{}^{\mathrm{+}}$, $\text{(}\text{1}\text{2}\text{)}{}^{\mathrm{?}}$, $\text{(}\text{3}\text{2}\text{)}{}^{\mathrm{?}}$, $\text{(}\text{5}\text{2}\text{)}{}^{\mathrm{?}}$ and they are in a very good agreement with the experiment.     

The N = 2 supersymmetric generalization of the complex sine-gordon model

A two-dimensional field theoretical model endowed with a Lax pair and invariant under complex supersymmetry is written in a manifestly invariant formulation. The bosonic limit of the model reproduces the complex sine-Gordon equations [that is the reduced O(4) σ-model introduced by Pohlmeyer, Lund-Regge and Getmanov]. The supersymmetry algebra contains central charges which generalize the one found by Witten and Olive in the super sine-Gordon case.     

The L1L2,3V Auger transition in Si

The L₁L_2,3V Auger transition in silicon has been analyzed. No substantial differences are observed in the comparison with the deconvolution of the L_2,3VV Auger spectrum. Comparison is also made with other valence band spectroscopies. It is concluded that L₁L_2,3V transition has a band character.     

Chemical shifts of X-ray K or L-absorption edges of solids

A very simple method for the calculation of the chemical shifts of X-ray K or L-absorption edges of metals when they undergo chemical combination, is proposed. It has been found that the major contribution to the chemical shifts comes from the change in the Fermi energy when the metal forms a compound. Fairly good agreement in the nature and the numerical magnitude of the chemical shifts between the observed and calculated values has been obtained.     

L to M shell transitions and model comparisons for radiative opacities of sodium fluoride plasma

The radiative opacities of hot dense sodium fluoride (NaF) plasma have been studied in the case of local thermodynamic equilibrium (LTE). The spectrally resolved opacity in the case of and is taken as an example to illustrate the absorption structures of the NaF plasma. The transitions from L to M shells of sodium and fluoride are the main contributions for the plasma absorptions. The isodense opacities of NaF plasma are studied at a density of and temperatures of 20-60 eV. Detailed comparisons among the results of the detailed term accounting (DTA), detailed configuraion accounting (DCA), unresolved transition array (UTA) and average atom (AA) model codes, which have been developed independently in China in the past few years, are performed for both the spectral resolved and mean opacities. Good agreements are found at a temperature of 40 eV and a density of , but discrepancies appear at a temperature of 50 eV and a density of .     

Instanton effects in N = 2 supersymmetric quantum mechanics

Supersymmetric quantum mechanics with several bosonic and fermionic dynamic variables is considered. Two different N = 2 supersymmetric models involving instantons are discussed in detail. Instantons fail to break supersymmetry in one of the models considered. The vacuum state is degenerate in this model which generally results in spontaneous breaking of internal left-right symmetry. In another model supersymmetry is destroyed dynamically due to special complex instanton solutions. Possible implications for SUSY field theories are discussed.     

Low energy constraints on N = 2 supersymmetric models

We derive constraints on the masses of mirror particles in N = 2 supersymmetric theories. We consider the K_L?K_S mass difference, the π → ev/π → μv branching ratio and the anomalous magnetic moment of the muon. The K_L?K_S mass difference gives a lower bound of 15 TeV on the mirror gauge scalar and mirror gauge fermion masses, under suitable assumptions.     

Conformal invariance in N = 4 supersymmetric Yang-Mills theory

It is shown, by consideration of anomaly multiplets, that the maximally extended supersymmetric Yang-Mills theory is conformally invariant, assuming that the theory is supersymmetric and O(4)-invariant and that the structure of anomalies is given by the breakdown of conformal invariance in its coupling to supergravity.     

N = 2 supersymmetric Yang-Mills theory and its supercurrent

Using the off-shell two-component formulation of N = 2 supersymmetric Yang-Mills theory and the gauge covariantized supersymmetry transformations for the fields, the non-abelian supercurrent and anomaly multiplets are developed and the transformation rules for their components are obtained. The superfields in N = 2 superspace whose components are the non-abelian supercurrent and anomaly multiplets are written down.     

The anomaly in the Slavnov identity for N = 1 supersymmetric Yang-Mills theories

We solve the consistency conditions of the BRS symmetry in a general N = 1 sypersymmetric Yang-Mills theory with semi-simple gauge group. As a result we find uniquely the supersymmetric extension of the chiral anomaly. Its coefficient is calculated in one loop and does not, in general, vanish. This corrects our earlier statement on the absence of this anomaly.