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 model regularizing gauge fields in the strong coupling region

We propose a model using an effective lagrangian for bilocal gauge extended fields, looking somehow as an average over all open strings with fixed end points. The locality of the action is retrieved as a range parameter, which acts as a regulator, shrinks, and the Yang-Mills theory is recovered in this limit. The system is invariant by rotation and translation, generalizes lattice gauge theories and allows regularized strong coupling expansions for Yang-Mills field theory.     

Interacting field theory of open superstrings

A proposal for a gauge invariant nonlinear classical field theory of open superstrings is explored. The gauge fixing that gives rise to the standard structure in the Ramond sector is described, answering questions that have been raised in recent literature. The model is shown to possess space-time supersymmetry as well as gauge invariance. The proof of space-time supersymmetry uses the covariant form of the fermion emission vertex and the associated picture changing operation, in accord with suggestions by several authors. Also discussed are the canonical formulation of the theory, and some issues connected with the extension of the work to closed strings.     

General relativity as a conformally invariant scalar gauge field theory

The global symmetry implied by the fact that one can multiply all masses with a common constant is made into a local, gauge symmetry. The matter action then becomes Conformally invariant and it seems natural to choose for the corresponding scalar gauge field the action for a conformally invariant (massless) scalar field. The resulting conformally invariant theory turns out to be equivalent to general relativity. Since this means that the usual Einstein-Hilbert action is not, in fact, a true gauge action for the space-time geometry, the full theory ought to be supplied with such a term. Gauge-theoretic arguments and conformal invariance requirements dictate its form.     

Gauge invariant actions of free closed superstring field theories

A gauge invariant action of free N=1 closed superstring field theory is presented using BRS charges. This action is shown to take a similar form to that of open superstring. The N=2 closed superstring is also discussed.     

Equivalence between the unified dual model and Pomeron-Reggeon amplitudes

We show that a recently proposed unified dual model for interacting open and closed strings actually describes Pomeron-Reggeon amplitudes of the conventional Veneziano model. We prove, in particular, that the Pomeron amplitudes are given by the Shapiro-Virasoro model.     

Field theory of the interacting string: The closed string

We recast dual models in the language of a quantum field theory of functional fields, restricting ourselves for simplicity to the closed string model. We derive the dynamics for both scalar and spinor functional fields from a unique parametrization invariant action. Passages to the Hamiltonian formalism and second quantization are explicitly worked out for the closed mesonic string in the front form. The results are equivalent to those obtained earlier by GGRT, i.e. no ghost fields at the price of an anomalous number of space-time dimensions and a tachyon. Finally, we use the parametrization invariance requirement on the action to derive couplings of closed strings to local fields by extending a global U(1) invariance built in the free action into a local one in the functional sense. We construct the self-couplings of closed string fields by requiring these to be consistent with the gauge invariance of the external fields. This procedure uniquely leads (for the open string) to the string splitting picture of Nambu and Mandelstam. The closed string is found to cross itself and then split up into two others. Both open and closed strings have quartic interactions corresponding to strand (for the open string) and lobe (for the closed string) exchanges. The case of the interacting fermionic model is not treated here.     

Quantization of chiral gauge theories in two-dimensions

It is shown that both abelian and non abelian chiral gauge theories in two dimensions can be made gauge invariant at the quantum level by adding a scalar field. In the bosonized form of the theory, the scalar field appears in a gauged Wess-Zumino action. The current algebra of the extended abelian theory is shown to be free of anomalous terms.     

Chiral Schwinger model with new regularization

A recently proposed version of the chiral Schwinger model is studied in detail in this paper. It is shown that a suitable Pauli-Villars regularization can be devised to reproduce the bosonized form of the effective action that was earlier written down. It is then shown how this anomalous gauge theory can be made gauge invariant by the introduction of a Wess-Zumino field. The equations of motion of this theory are explicitly solved in Lorentz covariant gauges. Finally, the operator solution of the fermionic form of the theory is constructed.     

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 g₀²n 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 g₀²n. A possible extension to fermionic strings, and the implications for large-n gauge theories are briefly discussed.     

Evolution of Nielsen-Olesen''''s String from Chern-Simons Field Theory

We study the topology of Nielsen-Olesen's local field theory of single dual string. Based on the Chern-Simons field theory in three dimensons, we find many strings that can form world sheets in four dimensions. These strings have important relation to the zero point of the complex scalar field. These world sheets of strings can be expressed by the topological invariant number, Hopf index, and Brower degree. Nambu-Goto's action is obtained from the Nielsen's action definitely by using o-mapping theory.     

Evolution of Nielsen-Olesen's String from Chern-Simons Field Theory

We study the topology of Nielsen-Olesen's local field theory of single dual string. Based on the Chern-Simons field theory in three dimensons, we find many strings that can form world sheets in four dimensions. These strings have important relation to the zero point of the complex scalar field. These world sheets of strings can be expressed by the topological invariant number, Hopf index, and Brower degree. Nambu-Goto's action is obtained from the Nielsen's action definitely by using φ-mapping theory.     

Homotopy Classification of Bosonic String Field Theory

We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.     

Off shell states in the dual model

We present a class of Lorentz invariant, gauge invariant off-shell amplitudes for the ordinary Veneziano and Ramond-Neveu-Schwarz dual models. They correspond to interactions with the string which are local in space-time.     

Loop variables and gauge invariant exact renormalization group equations for (open) string theory

An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non-zero mass is essential for this. This is reminiscent of Abelian Born–Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of the field strength.     

String model with baryons: Topology; classical motion

We consider the model in which a meson is an open string with a quark at one end an anti-quark at the other end; a baryon is made of three strings joining at a point, and carrying quarks at their free ends. The triality condition is ensured by orienting the strings according to simple rules. These rules suggest the existence of an underlying magnetic monopole theory. Independently of this “explanation”, we investigate first the topological properties of the model, by looking at the duality diagrams: existence of exotic hadrons, of five basic interactions between strings. Some renormalization diagrams are assigned a negative power of the Veneziano coupling constant. Then, taking the same action (the world-sheet area) as in the conventional string model, we set down the equations of motion of a junction. We argue that the slope of the leading baryonic Regge trajectory is the same as that for the mesons. As an example of an application, we study the “sticking together” of two colliding strings; we find that it is classically forbidden at relative velocities greater than $\text{(}\text{6}\text{7}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$.     

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N   of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3$N?3$ part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.     

Modified strings in terms of zweibein fields

Possible modifications of the relativistic string which preserves conformal invariance in the conformal gauge is investigated using zweibein fields. A fully reparametrization-invariant action yielding Liouville's equation is then constructed without the introduction of auxiliary fields. This action breaks the local two-dimensional Lorentz invariance and the corresponding extra degree of freedom reduces in the conformal gauge to a free field. For open strings the variation of the action implies that the Liouville field and this free field are connected by a Bäcklund transformation at the boundary. In certain cases it is shown that this extends to hold everywhere. If the local Lorentz invariance is restored, then the reparametrization algebra acquires the anomalous term necessary for the quantization in subcritical dimensions.     

A FIELD THEORY MODEL FOR CLOSED BOSONIC STRINGS

Besed on the BRST approach to the first quantization of closed bosonic strings, we propose a gauge covariant field theory model for both free and interacting closed bosonic strings. The action is of the Chexn-Simons type and coincides with the cohomology of the BRST operators.