Veneziano Model Research Articles

SEMI-FREE FIELD REPRESENTATION AND STRING FIELD THEORY IN 2D GRAVITY

String field theory for 2D gravity coupled to a c=1 matter field is described. We use the free field representation and take into account the semi-bounded of the Liouville mode in the last step of calculations. We call such representation semi-free field representation. It is shown that the Witten string field theory gives a tachyon action which up to some, factor in the interaction term coincides with the Das-Jevicki-Polchinski action. Starting from string field theory with semi-free field representation we calculate string amplitudes. These amplitudes instead of energy conservation δ-functions contain energy denominators which residues coincide with the Veneziano (Shapiro-Virasoro) amplitudes for open (closed) string and exhibit very interesting property: the s, t and u poles become the poles in respect to individual external momentum. These poles are related with higher levels excitations living only with fixed momentum.

Particle theories with minimum observable length and open string theory

We investigate a class of particle theories that have minimum observable length. Among them we find the theory equivalent to the open bosonic string theory. For this theory, starting from a reparameterization invariant and non-local action with respect to a world-line parameter, we derive the Virasoro constraint and the Veneziano amplitude. The possible relation to other attempts to introduce a fundamental length scale into particle theory is also discussed.

Shapiro-Virasoro amplitude and string field theory.

One of the embarrassments of covariant string field theory has been the glaring failure to derive the Shapiro-Virasoro amplitude. Modular invariance appears explicitly violated: either the fundamental region is overcounted an infinite number of times, or it is undercounted because of a missing region. We try to approach this problem from a fresh point of view. Conventional wisdom holds that, in string field theory, the Veneziano amplitude can only be derived either in light-cone string field theory or Witten's string field theory. We show that this firmly held belief is actually wrong, that the Veneziano amplitude can actually be derived using vertices of arbitrary lengths. This is a highly nontrivial calculation. Using third elliptic integrals we show that a series of ``miracles'' occurs which allow us to cancel scores of unwanted terms in the measure, leaving us with the correct Koba-Nielsen variable and measure. We give three independent proofs of our result. When we generalize our results to closed-string scattering with arbitrary lengths, we find a new surprise, that we can successfully derive the Shapiro-Virasoro amplitude as long as a crucial four-string interaction term is added. We check by explicit computer calculation that we reproduce the correct region of integration for the four-closed-string amplitude. Crucial to the theory is the existence of the missing four-string tetrahedron graph, which precisely fills the missing integration region. We comment on the implications of this for geometric string field theory.

Q-deformation of SU(1,1) conformal ward identities and q-strings

We define a q-deformation of the SU(1, 1) Ward identitied of 2D conformally invariant field theory based on the quantum SU(1, 1) algebra. The deformation preserves the main properties of the conformal Ward identities, namely that the two- and three-point functions are completely determined. A connection with a q-deformation of the Veneziano amplitude is revealed.

On the adelic string amplitudes

Some remarkable properties of the adelic string amplitudes for the physical domain of the Mandelstam variables are considered. It is shown that the p-adic four-point functions are always negative. Also, a formula is obtained which expresses the product of moduli of the p-adic amplitudes and the Veneziano amplitude in terms of the zeta functions. This product is absolutely convergent unlike the divergent product of these amplitudes without moduli, recently considered by Freund and Witten. Using the zeta function representation, p-adic interpolation of the Veneziano amplitude is also considered.

Harmonic analysis and p-adic strings

A generalization of the Veneziano amplitude is considered which is a convolution of two characters on a field K. Choosing K in an appropriate way, one can obtain the usual Veneziano amplitude, the Virasoro-Shapiro amplitude, the p-adic amplitudes, and the finite Galois field amplitude. The cases when K is an algebra or a group are also discussed. These cases can be of interest in the context of the quantization of spacetime.

P-Adic strings, the Weil conjectures and anomalies

An analogy between the Veneziano amplitude and the p-adic interpolation of the beta-function is suggested as the basis of a new p-adic quantum geometry. Relationships with the Weil conjectures, Fermat curves and anomalies are discussed.

Interacting quasiopen strings.

A 26-dimensional quasiopen string, in which Poincare invariance in some dimensions is broken by new boundary conditions, has also a new mass spectrum. Based on locality we construct vertex operators and generalized dual Veneziano amplitudes with singularities corresponding to the quasiopen mass spectrum.

P-adic space-time and string theory

Arguments for the possibility of a p-adic structure of space-time are advanced. The p-adic analog of the Veneziano amplitude is proposed, and this permits a start to be made on the construction of the theory of p-adic strings. The same questions are considered over Galois fields, for which the analog of the Veneziano amplitude is a Jacobi sum that can be expressed in terms of p-adic cohomologies of Fermat curves. An explicit expression for the vertex operator of the corresponding string theory is given.

Nonplanar loops leave the Veneziano model photon massless

The absence of a pole at p 2=0 in the orientable nonplanar one-loop photon self-energy in the Veneziano model is verified. Thus the photon remains massless, and spontaneous symmetry breaking - at least as reported in this context in the literature - is not found.

The Veneziano amplitude from interacting string field theory

The Veneziano amplitude is derived from a gauge invariant interacting string field theory recently proposed to describe the open bosonic string. This is accomplished by conformally mapping the four-string world-sheet to the upper half-plane.

A non-perturbative study of regularized bosonic string amplitudes

The Wick-rotated, light-cone gauge U( n) Veneziano model of open and closed strings is examined in the limit as n → ∞, with g 0 2 n fixed. The amplitudes in both the “pomeron sector” (whose graphs are cylinders with holes punched out) and the “reggeon sector” (whose graphs are rectangles with holes punched out) are regularized using the lattice method of Giles and Thorn, as well as an alternative method. It is found that this string model is trivial. When the cut-off is removed, the pomeron and reggeon sector spectra are those of the free closed and open strings, respectively. This result is independent of the choice of g 0 2 n. A possible extension to fermionic strings, and the implications for large- n gauge theories are briefly discussed.

Non-commutative geometry and string field theory

An attempt is made to interpret the interactions of bosonic open strings as defining a non-cummulative, associative algebra, and to formulate the classical non-linear field theory of such strings in the language of non-commulative geometry. The point of departure is the BRST approach to string field theory. A setting is given in which there is a unique gauge invariant action, whose linearized approximation reproduces the conventional Veneziano spectrum. A derivation of conventional Veneziano model amplitudes from this gauge invariant action is sketched. Some brief comments are made about attempts to extend these results to open superstrings and to closed strings.

Anomaly cancellation and fermionisation in 10-, 18- and 26-dimensional superstrings

The gauge and gravitational anomalies of a generic superstring are shown to vanish in four cases: the known E 8 2 and E 16 models in dimension 10; a new E 8 model in dimension 18 and a Giant model in dimension 26. New modular identities show that the Giant can be supersymmetric, and that the E 8 model can be constructed in two equivalent ways, either as a Neveu-Schwarz-Ramond model or via a Nahm-Freund fermionization of the solitons of an E 8 compactified Veneziano model.

Covariant string theory Feynman amplitudes

The covariant string amplitudes on a strip with the associated Feynman rules are considered. The contribution of the Faddeev-Popov ghost is evaluated. The overlap vertex (coming from a δ-function interaction) is constructed. The corresponding scattering diagrams are shown to give the standard Veneziano model answer. The ghosts provide the necessary contribution to the measure.

String models with lower critical dimension, compactification and nonabelian symmetries

We discuss certain aspects of dimensional compactification in bosonic string models which might be generalized to the superstring case. In dual models of the Bardakci-Halpern type the critical dimension can be lowered in the presence of nonabelian symmetries. The same relation between critical dimension of Minkowski space and the rank of the nonabelian gauge group appears in the Veneziano model with some dimensions compactified on the group manifold. In ten dimensions one of the solutions is O(32).

Bag-Like Model for Hadrons and Its String-Like Properties

A specific bag-like model is proposed, in which quarks and gluons are confined in hadrons by an infinitely deep square-well potential of the spherical shape. In order to clarify various properties of our model in a framework of the field theory by using the soliton theory, the SU(2) Higgs-Kibble-like model is considered as a simple toy model of QeD. By the effect of the classical solution for an isospin singlet component of a complex isospinor scalar field, our confining potential is derived. It is shown that our model of hadrons has almost the same properties as the string model does, i. e., the infinite degeneracy of the internal states, the approximately linearly rising Regge trajectory (in the low energy region) and the Veneziano amplitude. These properties are derived from the contribution of the gluons only.

Study of the reaction π-p → ψn in generalized Veneziano models

Study of the reaction π-p → ψn in generalized Veneziano models

Reggeon field theory (Schlögl's first model) on a lattice: Monte Carlo calculations of critical behaviour: P. Grassberger and A. de la Torre. Faculty of Physics, University of Wuppertal, Germany

A method is suggested for calculating the elastic amplitude as the shadow of multiparticle processes. This does not require explicit formulae for the production amplitudes, but depends only on the following assumptions: (a) Regge behaviour, (b) semi-local duality, (c) exchange degeneracy. The system is multiperipheral in general structure but because of the assumption (a)-(c), it incorporates such features as the clustering of final particles and provides a proper treatment of quantum numbers, phases, and resonance spins. As a result, the unitarity sum separates automatically into two components corresponding respectively to pomeron and ordinary reggeon exchange, each of which is seen to have the correct qualitative dependence on the quantum numbers, the energy s, and the momentum transfer t. Quantitatively, the elastic amplitude is given in terms of a triple-Regge vertex, for which we suggest a simple parametization based on a detailed study of existing experiment and the Veneziano model. The method is then applied to calculate the elastic amplitudes for π±p, K±p and pp within the range 6 < s < 50 and 0 > t > −0.5 GeV2. Semi-quantitative agreement is obtained with experiment with essentially no free parameter. Although the investigation is restricted at present to elastic scattering as the shadow of only the non-diffractive component satisfying (a)-(c), the method is believed to apply also to other diffractive processes, and may be regarded as the first step in an iterative solution of the full unitarity equation.

Can theππscattering amplitude be represented by any Veneziano model?

We propose a general definition of a Veneziano-model amplitude in terms of the support property of its double inverse Laplace transform. A practical test of this property is then formulated and applied to $\ensuremath{\pi}\ensuremath{\pi}$ scattering. It is satisfied by the nonexotic $\ensuremath{\pi}\ensuremath{\pi}$ amplitudes but not by the exotic ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$ scattering amplitude. However there are significant deviations from the explicit Lovelace-Shapiro model and the isovector-exchange amplitude is better represented by the symmetric-group model of Frampton.