General Class Of Theories Research Articles

Instability of fermionic zero modes and dynamical supersymmetry violation

We investigate the Dirac operator of massless and partially massless supersymmetric theories in four dimensions. We find that for a very general class of theories, all zero modes disappear from the spectrum under a generic variation of the scalar background field. The reason is the impossibility of maintaining a normalizable asymptotic behavior both at the origin and at infinity. As an application, we prove that the vacuum energy density of a large class of supersymmetric theories is strictly negative, a phenomenon which signifies a dynamical violation of the SUSY algebra. Certain implications for the anomaly equation as well as for completely massive theories are also discussed.

Pomeron intercept in a general class of Reggeon field theories

The mechanism of the vacuum instability, which, as shown by Abarbanel, Bronzan, Schwimmer, and Sugar, prevents the Pomeron intercept from rising above 1 in a theory with a triple-Pomeron interaction, is shown to operate in a general class of theories which satisfy some (plausible) conditions of positivity.

Neutrino electron scattering in theories with neutral currents

Elastic neutrino electron scattering is considered in a general class of theories containing both charged and neutral currents. Assuming μ-e symmetry, the following results are proved. 1. (i) σ(ν ee ) + σ(ν μ e) ⩾ 2 , 2. (ii) σ( ν ee ) + σ( ν μ e) ⩾ 1 2 , 3. (iii) σ( ν ee ) − σ( ν μ e) = 1 3 [σ(ν ee ) − σ(ν μ e)] , 4. (iv) |[σ(ν ee ) − 1 3 [σ(ν ee )] 1 2 ± [σ( ν μ e) − 1 3 σ( ν μ e)] 1 2 |= 4 3 , (where cross sections are in units of G 2 mE ν / π). Constraints are derived on the energy spectrum of the recoil electron. The Weinberg-Salam theory and the V-A theory are considered as special cases.