Neveu-Schwarz Model Research Articles

On the N-pion extension of the Lovelace-Shapiro model

We reconsider a modification of the N-point amplitude of the Neveu-Schwarz (NS) model in which the tachyon becomes a pion by shifting its mass to zero and keeping the super-projective invariance of the integrand of the amplitude. For the scattering of four particles it reduces to the amplitude written by Lovelace and Shapiro that has Adler zeroes. We confirm that also the N-pion amplitude has Adler zeroes and show that it reduces to that of the non-linear σ-model for α′ → 0 keeping Fπ fixed. The four- and six-point flavour-ordered amplitudes satisfy tree-level unitarity since they can be derived from the correspondent amplitudes of the NS model in ten dimensions by suitably choosing the components of the momenta of the external mesons in the six extra dimensions. Negative norm states (ghosts) are shown to appear instead in higher-point amplitudes. We also discuss several amplitudes involving different external mesons.

Ramond and Neveu–Schwarz paraspinning strings in presence of D-branes

We investigate the theory of an open parafermionic string between two parallel Dp-, Dq-branes in Ramond and Neveu–Schwarz sectors. Trilinear commutation relations between the string variables are postulated and the corresponding ones in terms of modes are derived. The analysis of the spectrum shows that one can again have a free tachyon Neveu–Schwarz model for some values of the order of the paraquantization associated to some values of p and q. The consistency of this model requires the calculation of the partition function and its confrontation with the results of the degeneracies. A perfect agreement between the two results is obtained and the closure of the Virasoro superalgebra is confirmed.

Digitizing the Neveu-Schwarz model on the lightcone worldsheet

The purpose of this article is to extend the light-cone worldsheet lattice description of string theory to include the Neveu-Schwarz model. We model each component of the fermionic worldsheet field by a critical Ising model. We show that a simple choice of boundary conditions for the Ising variables leads to the half-integer modes required by the model. We identify the $G$-parity operation within the Ising model and formulate the procedure for projecting onto the even $G$-parity sector. We construct the lattice version of the three open string vertex, with the necessary operator insertion at the interaction point. We sketch a formalism for summing planar open string multiloop amplitudes, and we discuss prospects for numerically summing them. If successful, the methods described here could provide an alternative to lattice gauge theory for computations in large $N$ QCD.

Hurwitz duality theorems for Fueter and Firac equations

The paper aims at proving general duality theorems for Hermitian Hurwitz pairs (abbreviated as HHP), related to the generalized Dirac or Fueter equations, and gives comparison theorems for solutions of #-self adjoint Dirac or Fueter equations, where #-self adjointness implies the self adjointness with respect to certain indefinite metrics. In low-dimensional cases these duality theorems can be described in a more explicit manner. Namely, we can get dualities between the Minkowski space-time with signature(+, − − −) and the neutral space with signature (++, −−) related to the Penrose theory. We can also get the dualities between the Neveu-Schwarz model with (+,−) and the holomorphic-antiholomorphic model with (−, −). These dualities can be described in terms of the Wick rotations. We notice that the Wick rotation cannot be used directly because our Dirac operators are #-self adjoint, while the Wick rotations break down this property.

Vertex operator superalgebras

In this paper, we construct the action of super vertex operators In section 1, we construct a Fock space V for a 2l-dimensional C-vector space A. In physics, V appears as the Fock space of Neveu-Schwarz model of dual poins. See Neveu-Schwarz [5]. In mathematics, V appears as the spin representation space of the affine Lie algebra&ŝ2l. See Frenkel [2] and [3]. In section 2, we define a super vertex operator A V,Z : V→V[[z,z-1]] for each element v of the Fock space V. The most important property of the super vertex operators is the so-called associative law. Using this law, we can see that the coefficients v n : V→V in A v,z span a Lie superalgebra and explicitly write down the Lie superbackets in section 3. It is a huge Lie superalgebra called the vertex operator superalgebra of A.

Three-reggeon light-cone vertex of the Neveu-Schwarz string

We construct in the superfield formalism the vertex operator corresponding to the most general physical state of the Neveu-Schwarz model. These vertex operators are then used to compute the on-shell three-reggeon vertex.

Covariant fermionic vertex in superstrings

A covariant fermionic vertex is constructed in terms of Ramond spinors and ghost operators, starting from the Neveu-Schwarz model. Correlation functions of spinors and ghosts are defined. The supersymmetry algebra is realized as the algebra of massless vertices with zero momentum.

Superfield Approach to Systems of Two and Three Spinning Particles

Systems of two and three spinning particles are investigated by regarding each particle as a superfield defined in a two-dimensional superspace. It is shown that the resultant systems become respective bi-local counterparts of the Neveu-Schwarz model and the Ramond model in the dual model theory. Short comments on the massive particle and the interaction with an external gauge field are also given.

Diffractive dissociation in the dual model

We study the one twisted loop contribution to the five-point function in the Neveu-Schwarz model. The formulation obtained incorporates the requirements of duality and analyticity (Steinmann relations), provides a low-mass vector-pseudoscalar system predominantly as an S-wave J P = 1 + state near threshold, conserves approximately t-channel helicity and thus is an interesting candidate for the phenomenology of diffractive dissociation.

Partially conserved axial-vector current inS-matrix theory

Mandelstam’s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm π andm ϱ as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionmϱ2−mπ2=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.

Possible phenomenological implications of the new trajectories on the pion trajectory

We discuss possible phenomenological consequences of the new Regge trajectories recently discovered in the conventional dual model (CDM) and the Neveu-Schwarz model (NSM). The contributions of the new trajectories to the scattering amplitude dominate at large enough momentum transfers in the multi-Regge limit and it is shown that the β π trajectory of the NSM should be the most easy to detect experimentally.

Towards a Satisfactory Invariant Measure of Dual-Resonance Amplitudes

An attempt is made, in the context of the integral representations of the four-point dual amplitudes, to lower the critical degree of space-time dimensions on which dual amplitudes are established. The critical dimension and the intercept of the leading Regge trajectory are determined by an invariancy (under a dual operation) of a differential form (including a volume element), which thus plays a role of measure. A derivation is given of a measure a la Nahm which yields the worldly dimensions in such a way that it appears as a natural generalization of that of the Neveu-Schwarz model, hence still suffering from a presence of tachyon. Its relevancy is studied within the simplest case of two off-shell dual amplitudes. Also specified is the modular group associated with the new volume element. The volume element points to a new pair of the fermi-type dynamical fields, whose construction has not, however, been tried.

A gauge mapping theorem for the spinning string in an orthonormal gauge

It has been proved that the canonical co-ordinates for a classical «spinning» string in an orthonormal gauge are the canonical co-ordinates for all gauges. These canonical co-ordinates have been shown to be a generalization of the classical analogues of the DDF operators of the Neveu-Schwarz dual model.

Quantization of a massless spinning string in a timelike gauge

The quantization programme for a massless relativistic spinning string in a timelike orthonormal gauge has been worked out in the manner of Goddard, Hanson and Ponzano using Dirac’s approach by constructing classical analogues of DDF-type operators of the Neveu-Schwarz dual-resonance model. The programme has been shown to be completely equivalent to that in a lightlike orthonormal gauge. The canonical quantization is seen to be possible only in 10, space-time dimensions with the value of the Regge intercept of 1/2.

Supergauge Algebra and Interaction between Open and Closed Strings

In the Neveu-Schwarz and Ramond models we construct the vertices which describe the emission of closed-string ground-state particles out of open string states. The modified supergauge algebra associated with the new vertices can be shown to hold in the same form as the usual supergauge algebra in free cases. and is crucial for proving the no-ghost theorem in our system.

Grassmann Algebraic Approach to the Neveu-Schwarz Model and Representation of Super-Mobius Algebra

On the basis of new integral representation proposed by Fairlie and Martin, we develop a manifestly super-gauge invariant formulation of the Neveu-Schwarz model. We show that the Fairlie-Martin representation is invariant under wider trafisformations (super-Mobius transformations) than the usual Mobius transformations. The corresponding algebra (super­ Mobius algebra) is a closed subalgebra of the super-gauge algebra. The operator formalism is reconstructed as a representation of the super-Mobius algebra. As a generalization of our formulation, we introduce closed-string emission vertices for the Neveu-Schwarz open-string which are manifestly covariant under the super-gauge transformations as well as the confotmal transformations. Finally we discuss briefly the general representation theory of .the s~per­ Mobius algebra. Unfortunately, the representation appeared in the Neveu-Schwarz model is essentially unique as the representation of the full super-gauge algebra. However, two types of_ the mass spectrum are possible.

The pomeron and other single dual loops without unphysical states

We recalculate the single nonplanar dual loop in the critical dimension of space-time. This becomes possible because of our recent analysis of the nature of physical states in the dual model which enables us to understand whenτ(k), the on-shell projection operator of Brink and Olive, becomes Lorentz covariant. We calculate the « pomeron » loop and show that the pomeron becomes a factorizable pole in the critical dimension, as previously conjectured. We indicate how our results extend to the Neveu-Schwarz model.

Ghost-Free Two-Body Scattering Amplitudes with Arbitrary External Masses

Schwarz's method to construct off-mass-shell amplitudes is extended to two-body scatter­ ing amplitudes with arbitrary external masses in the Veneziano and Neveu-Schwarz models. It is shown that ghost-free amplitudes are obtainable by replacing linear t-channel trajectories by s-dependent ones in the Veneziano amplitudes and the Neveu-Schwarz ones respectively. It is also shown that transversely polarized integer spin particles can be introduced as one of initial or final two particles. In particular an application of our method to virtual Com­ pton scattering amplitudes reveals that the longitudinal parts vanish identically.

Interacting fermionic and pomeronic strings: Gravitational interaction of the Ramond fermion

We present a ghost-free model for the Ramond fermion interacting with closed and open bosonic strings. Since a closed string contains a «graviton» state as a physical state, which reduces to the Einstein graviton in the zero-slope limit, we introduce the interaction of the closed-string graviton with the fermionic string of Ramond in a way analogous to the usual tetrad formalism for the interacting gravitational and spinor fields. By considering the general co-ordinate transformation and the local Lorentz transformation for the fermionic string, we obtain the vertex for an external tetrad field. We show that the vertex satisfies desirable gravitational and supergauge properties. A general form of the vertices describing the emission of the closed string out of the fermionic string is given by extracting the gauge properties of the graviton vertex. In our model, the self-interaction among the closed strings is described by the nonplanar version of the Neveu-Schwarz model. The zero-slope limit of our model is also briefly considered.

Predictions of Quark and Dual Approaches to Meson Classification

At the six lowest-lying levels, the quark model predicts a sequence $L=0, 1, 2, \dots{}$ of meson states with specific ${J}^{\mathrm{PC}}$ coupling to two and three pions. The symmetric-group model gives exactly the coincident prediction for the ${J}^{\mathrm{PC}}$ sequence. The Neveu-Schwarz model is missing two states at these levels; the new states, predicted by both dual and quark models, are the ${J}^{\mathrm{PC}}={0}^{++}$, $^{3}P_{0}$ isoscalar daughter of $f(1250)$, and the ${J}^{\mathrm{PC}}={1}^{+\ensuremath{-}}$, $^{1}P_{1}$ isoscalar partner of $B(1235)$.