Neveu-Schwarz Model Research Articles

Spontaneous symmetry breakdown and Regge intercepts

By Regge slope methods we exhibit a Nambu-Goldstone spontaneous symmetry breakdown and a Higgs mechanism inherent in a unit-intercept dual meson amplitude. Introducing an Abelian gauge group corresponding to conservation of a pseudocharge, Regge intercept shifts are calculated; to lowest order the leading Regge intercept of the Neveu-Schwarz model is lowered from α(0) = 1 to α(0) = 1 2 . Our method has the advantage over Bardakci's spurion method that massless scalar are not required at any stage.

Multi-Regge limit of the Neveu-Schwarz model

The structure of the Neveu-Schwarz model in multi-Regge limits is studied, with particular emphasis on quantum-number effects on Reggeon-particle vertex functions.

The scattering amplitude for four dual fermions

The amplitude for the scattering of four dual fermions is written down and evaluated in terms of three complicated functions. One of these is then expressed in terms of the other two. The s-channel spectrum is that of the Neveu-Schwarz model, but it is not possible at present to describe the t-channel spectrum. The spinor structure of the amplitude is also discussed.

The absence of ghosts in the dual fermion model

The consistency of the dual fermion model is further explored by showing the completeness of the transverse fermion physical states, in various situations, when the fermion ground state mass is zero. To this end the fermion physical state projection operator is constructed. A detailed direct proof of the absence of ghosts is given. The absence of fermion ghosts in twisted configurations is shown to require delicate cancellations. Comparison with the Neveu-Schwarz model indicates possible difficulties with the twisting operator.

Multiloop amplitudes in additive dual-resonance models

A technique is developed by which general multiloop amplitudes in additive dual-resonance models can be calculated, with spurious states propagating internally in the loops, however. The result shows the same automorphic structure as has been found in the Veneziano model. The case of the Neveu-Schwarz model is considered in more detail.

New light on the Neveu-Schwarz model

The Neveu-Schwarz model is revealed as possessing the same Koba-Nielsen structure as the original dual-resonance model in a formalism where the Koba-Nielsen variables are extended by the incoporation of anticommuting variables.

One-current amplitudes in the model of Neveu and Schwarz

Operators representing evenG-parity scalar and conserved vector currents and an oddG-parity axial vector current are constructed and the corresponding one-current amplitudes evaluated in the Neveu-Schwarz dual-resonance model by means of a scheme proposed by Neveu, Scherk and Cremmer. The amplitudes satisfy planar duality and the axial vector current realizes a dual version of PCAC.

A simple physical interpretation of the critical dimension of space-time in dual models

The energy due to zero point fluctuations of the dual string is calculated and shown to be divergent. We make it finite by introducing a cut-off. The result is non-covariant but invariant under reparametrization, so one has to modify the classical Lagrangian so as to get a covariant result. It is then shown that this leads to the well-known relation relating the mass squared of the lowest state to the number of dimensions space-time. This result is independent of the cut-off and shows clearly the physical significance of the critical dimension of space-time. Similar considerations for the Neveu-Schwarz model are also discussed.

Quantization of a String of Spinning Material—Hamiltonian and Lagrangian Formulations

The dynamics of a relativistic string made of spinning material is discussed in two different formulations. The first is a manifestly covariant formulation under a gauge transformation. The second is a Hamiltonian formalism which enables us to make the transition from the classical to the quantum description in a coherent way. The Lagrangian is also constructed. The results of our investigations are as follows: (1) The mass spectra here coincide with those of the Neveu-Schwarz model. (2) The model is ghost-free. (3) The Poincar\'e generators ${\mathfrak{M}}^{\ensuremath{\mu}\ensuremath{\nu}}$ and ${\mathfrak{P}}^{\ensuremath{\mu}}$ are constructed. The quantization is shown to be consistent with Lorentz covariance if the dimension of space-time is 10 and the Regge intercept is \textonehalf{}.

Pomeron factorization in general dual models

We demonstrate that in each ghost-free dual model with one minor restriction, there exists a critical dimensionality of space-time in which the pomeron singularity becomes a factorizable Regge pole. In each model when this dimensionality is chosen, the pomeron emerges with twice the intercept and half the slope of the leading secondary (f) trajectory. We explicitly construct the pomeron propagator and the operator coupling the pomeron to the reggeon sector for the general dual model, including the lower-lying negative- G-parity pomeron in the Neveu-Schwarz model. Gauge identities and physical states in the pomeron sector are also investigated. In all of the dual models the pomeron form factors exhibit a generalized f dominance and modified Wu-Yang behavior.

Recalculation of the unitary single planar dual loop in the critical dimension of space time

Abstract The single planar dual-loop amplitudes are recalculated in the critical dimension of space time paying particular attention to the unitary property by ensuring that the only states propagating internally in the loop are those needed to factorize tree diagram residues in a positive definite way. The two new technical features which make this possible are 1. (i) our newly discovered physical state projection operator valid if the space-time dimension takes the critical value; 2. (ii) the use of Feynman's tree theorem whereby it is sufficient to have the above projection operator on the mass shell. The final result agrees with a previous conjecture in that it differs from the original calculations with unprojected propagators by two inverse power of a certain partition function. The results apply to both the ordinary dual model and the Neveu-Schwarz model.

Simple Nonadditive Dual Resonance Model

A nonadditive model with spin degrees of freedom but no internal symmetry is studied. It is necessary to work in a space of ten or more dimensions in order to obtain a Hermitian Hamiltonian. The model possesses physical-particle creation operators and, rather surprisingly for a nonadditive model, all trajectories are linear. In ten dimensions the model appears to be equivalent to the Neveu-Schwarz model, but the trajectories with half-integral intercept are obtained even though all our operators have integral $n$. The gauge conditions associated with the $L$ and $K$ algebras are almost certainly sufficient to remove all the ghosts.

The physical state projection operator in dual resonance models for the critical dimension of space-time

We present the physical state projection operator for the simple dual resonance model in twenty-six dimensions of space-time and unit intercept in two forms-(which are proved to be equivalent). One form obviously projects onto the so-called transverse states and the other obviously gives unity when inserted into any residue of a pole in a dual amplitude. Thus we explicitly verify the completeness of transverse states in 26 dimensions and have a weapon for constructing genuine unitary dual loop amplitudes (as shown in a second paper). We also present the corresponding results for the Neveu-Schwarz model.

Spectrum-Generating Algebra and No-Ghost Theorem for the Neveu-Schwarz Model

The no-ghost theorem of Brower for the conventional dual model (intercept ${\ensuremath{\alpha}}_{0}=1$) is extended to the Neveu-Schwarz model, and its spectrum-generating algebra is constructed. These conformally invariant generators (${A}_{n}, {B}_{s}$) are obtained by a systematic use of the gauges ${G}_{r}$. As a consequence it is demonstrated that particular dual models having resonances with positive-definite norms and masses are possible.

Lagrangian formulation and current algebra in the Neveu-Schwarz dual model

We study in some detail the field theory formulation in co-ordinate space of the Neveu-Schwarz model for theN-pion amplitude and for theN-pion emission from a single quark line. We then consider the problem of current algebra for the fermion and for the boson case. In particular for the boson case we find a class of axial currents which satisfy the localSU2×SU2 algebra with the isospin currents and the PCAC relation between external real states.

An empirical extension of the Neveu-Schwarz model

We show that the Neveu-Schwarz model takes a simple form in the Koba-Nielsen formulation, the integrand taking the form of a Pfaffian. We find empirically that it is possible to improve the spectrum while retaining the Pfaffian formulation. Though the form obtained for the amplitude is suggestive of an underlying operational construction we have not succeeded in finding such a formulation. The Adler condition is implemented in this model in a non-trivial manner.

Compatibility of the dual Pomeron with unitarity and the absence of ghosts in the dual resonance model

It is shown that the number of states coupling in the Veneziano model when the space time dimension, d, is 26 ( d = 10 for the Neveu-Schwarz model) is reduced in such a way that the Pomeron is probably a pole. A simple consequence of this counting is the absence of ghosts for d ⩽ 26 ( d ⩽ 10 for Neveu-Schwartz).

Two Faces of a Dual Pion-Quark Model. II. Fermions and Other Things

In the first paper of this title, a dual pion model formulated by one of the authors was shown to be equivalent to the pion sector of the dual quark model. Here we establish that the fermions are also the same. In addition, we show that the Neveu-Schwarz model is a dual quark model with a particular spin-spin interaction, and give the fermions of the "Pomeranchon-pion" model.

Generalization of the Neveu-Schwarz model to arbitrary intercept

Generalization of the Neveu-Schwarz model to arbitrary intercept