Analysis of an SU(8) model with a spin-1 2 field directly coupled to a gauged Rarita–Schwinger spin-3 2 field

In earlier work we analyzed an abelianized model in which a gauged Rarita–Schwinger spin-[Formula: see text] field is directly coupled to a spin-[Formula: see text] field. Here, we extend this analysis to the gauged [Formula: see text] model for which the abelianized model was a simplified substitute. We calculate the gauge anomaly, show that anomaly cancellation requires adding an additional left chiral representation [Formula: see text] spin-[Formula: see text] fermion to the original fermion complement of the [Formula: see text] model, and give options for restoring boson–fermion balance. We conclude with a summary of attractive features of the reformulated [Formula: see text] model, including a possible connection to the [Formula: see text] root lattice.

A LAGRANGIAN FOR THE CHIRAL (½, 0) ⊕ (0, ½) QUARTET NUCLEON RESONANCES

We study the nucleon and three N* resonances' properties in an effective linear realization chiral SUL(2)×SUR(2) and UA(1) symmetric Lagrangian. We place the nucleon fields into the so-called "naive" (½, 0) ⊕ (0, ½) and "mirror" (0, ½) ⊕ (½, 0) (fundamental) representations of SUL(2)×SUR(2), two of each — distinguished by their UA(1) chiral properties, as defined by an explicit construction of the nucleon interpolating fields in terms of three quark (Dirac) fields. We construct the most general one-meson–baryon chiral interaction Lagrangian assuming various parities of these four nucleon fields. We show that the observed masses of the four lowest-lying nucleon states can be well reproduced with the effective Lagrangian, after spontaneous symmetry breakdown, without explicit breaking of UA(1) symmetry. This does not mean that explicit UA(1) symmetry breaking does not occur in baryons, but rather that it does not have a unique mass prediction signature that exists, e.g. in the case of spinless mesons. We also consider briefly the axial couplings with chiral representation mixing.

GAUGINO CONDENSATION IN THE CHIRAL AND LINEAR REPRESENTATIONS OF THE DILATON

String effective theories with N=1 supersymmetry in four dimensions are the subject of this discussion. Gaugino condensation in the chiral representation of the dilaton is reviewed in the truncated formalism in the UK(1) superspace. By the use of the supersymmetric duality of the dilaton the same investigation is made in the linear representation of the dilaton. We show that for the simple case of one gaugino condensate the results concerning supersymmetry breaking are independent of the representation of the dilaton.

CHIRAL SYMMETRY AND OPERATOR MIXING IN LATTICE SU(N) THIRRING MODEL WITH SHIFT SYMMETRY

We formulate lattice SU (N) Thirring model in which two Wilson fermions describe the respective left- and right-handed components of the Dirac fermion in the continuum model. Only chirally projected half components of the Wilson fermions have four-fermion interaction. As to their non-interacting components, there exist shift symmetries discussed by Golterman and Petcher. Axial U (1) Ward-Takahashi identity is examined by weak coupling expansion. It is shown in all orders of the weak coupling expansion that the chiral limit is achieved by simply setting fermion bare mass equal to zero, and that a lattice operator has no mixing due to the Wilson masses with the operators of wrong chiral representation and of lower dimensionality.