From the first to the second quantized string theory

Starting from the hamiltonian formulation of the bosonic string we calculate the Feynman transition amplitude D. Inverting D we get the kinetic operator and thus the free field action.     

The covariant perturbative string spectrum

We provide generating functions for the perturbative massive string spectrum which are covariant with respect to the SO(9)$\mathit{SO}(9)$ little group, and which contain all the representation theoretic content of the spectrum. Generating functions for perturbative bosonic, Type II, Heterotic and Type I string theories are presented, and generalizations are discussed.     

The interacting gauge covariant bosonic string

The interaction of the gauge covariant open bosonic string is presented in oscillator form, and in functional form. In the latter form, the string is described by commuting and anticommuting coordinates. The interaction is essentially the condition that the strings should overlap.     

Gauge-fixing in covariant string field theory

We discuss the gauge-fixing procedure of the covariant formulation of the open bosonic string recently proposed by Neveu, Nicolai and West (the so-called finite set). We show that this theory has new symmetries. However, it does not seem possible to recover the correct number of physical degrees of freedom.     

String length and covariant string field theory

String length differentials are shown to arise naturally in a BRST hamiltonian approach to the closed bosonic string. A gauge-covariant quadratic action is proposed which is shown to lead to the correct equations of motion. The gauge covariant action is extended to including a three-string interaction vertex, with exact invariance under an extended transformation on the string fields.     

About the uniqueness of covariant string field theory

Symmetry laws are in general not sufficient to specify a correct second-quantized covariant string action. It is shown that an additional requirement is necessary in order to get the correct physical spectrum. From this the existence of a unique “minimal” action is discussed to which any formulation should reduce after integration over Lagrange multipliers.     

Manifestly covariant field theory of interacting string II

A manifestly covariant field theory is constructed for the interacting bosonic closed string, which possesses a very simple string action invariant under an inhomogeneous nilpotent BRS transformation. The physical on-shell scattering amplitudes in this theory reproduce the Koba-Nielsen amplitudes at the tree level.     

A covariant and gauge invariant string fragmentation model

We present a fragmentation model, designed in particular to treat the decay of strings formed in soft hadronic interactions. The fragmentation model is based on classical string theory: the simplest possible local, covariant, gauge invariant fragmentation law is assumed. A very elaborate resonance table for low mass cluster decay is used. Resonances have a continuous mass spectrum, only stable hadrons are on mass shell. We treat quark-antiquark strings as well as quark-diquark strings and also more complicated structures (like \(\bar q - qqqq\) ). A large amount ofe ⁺ e ^? and lepton-nucleon data are used to fix parameters and to test the model.     

New symmetries and ghost structure of covariant string theories

It is shown that there exists an infinite set of new symmetries of the previously given covariant string formulations. These symmetries have themselves an infinite set of hidden local symmetries and so on. A new physically equivalent further extended string action is given in which the infinite set of symmetries is most easily displayed. A quantization involving gauge fixing and ghosts of the various covariant string actions is given.     

How covariant closed string theory solves a minimal area problem

For a given genusg Riemann surface withn0 punctures (n3 forg=0) we consider the problem of finding the metric of minimal area under the condition that the length of any nontrivial closed curve be greater or equal to 2. The minimal area metrics are found for the case of all punctured genus zero surfaces and for many of the higher genus surfaces both with and without punctures. These metrics are induced by Jenkins-Strebel quadratic differentials. They arise from the string diagrams corresponding to restricted Feynman graphs of a closed string field theory action containing classical and quantum restricted polyhedra.Supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069     

The multiloop covariant tadpole operator and amplitudes for the bosonic string

An explicit expression is given for the covariant tadpole operator with an arbitrary number of loops, including the ghost zero mode contribution. Its integrand is recast in geometrical terms and is recognized to give the g-vacuum for the bosonic string recently discussed in the literature. By joining the g-tadpole to an N-reggeon vertex the general orientable dual amplitude with g loops is obtained.     

From conformal quantum mechanics on bordered Riemann surfaces to covariant string field theory

The Faddeev-Popov determinant of the reparametrization ghosts of the closed bosonic string on bordered Riemann surfaces is investigated. It is found that the standard ghost action has to be supplemented by additional boundary terms. These additional terms lead to a nontrivial ghost transition amplitude. It is shown that boundary variations of ghost transition amplitudes are generated by the ghost Virasoro operators. The relevance of the boundary variation operator for string field theory is illustrated. A new interpretation of the BRST operator in terms of boundary variations is obtained and the BRST invariance of the transition amplitudes is demonstrated. A generalization of the Siegel gauge of second quantized closed bosonic string field theory is presented.     

A covariant open bosonic string field theory including the endpoint and middlepoint interaction

Extending the usual endpoint and midpoint interactions, we introduce numerous kinds of interactions, labelled by a parameter λ and obtain a non-commutative and associative string field algebra by adding up all interactions. With this algebra we develop a covariant open bosonic string field theory, which reduces to Witten's open bosonic string field theory under a special string length choice.     

Effective action and Hawking flux from covariant perturbation theory

The computation of the radiation flux related to the Hawking temperature of a Schwarzschild black hole or another geometric background is still well-known to be fraught with a number of delicate problems. In spherical reduction, as shown by one of the present authors (Kummer) with Vassilevich, the correct black body radiation follows when two basic components (conformal anomaly and a dilaton anomaly) are used as input in the integrated energy-momentum conservation equation. The main new element in the present work is the use of a quite different method, the covariant perturbation theory of Barvinsky and Vilkovisky, to establish directly the full effective action which determines these basic components. In the derivation of Kummer and Vassilevich the computation of the dilaton anomaly implied one potentially doubtful intermediate step which can be avoided here. Moreover, the present approach also is sensitive to IR (renormalization) effects. We realize that the effective action naturally leads to expectation values in the Boulware vacuum which, making use of the conservation equation, suffice for the computation of the Hawking flux in other quantum states, in particular for the relevant Unruh state. Thus, a rather comprehensive discussion of the effects of (UV and IR) renormalization upon radiation flux and energy density is possible.Received: 17 October 2004, Revised: 11 January 2005, Published online: 21 February 2005PACS: 04.60.-m, 04.60.Kz, 04.70.Dy     

Dual models as saddle point approximations to Polyakov's quantized string

We show that if the metric becomes singular on the boundary, then Polyakov's quantized string theory has a saddle point. This leads to an off-shell Green function, the S-matrix of which is the standard dual (Veneziano) model.     

On the static potential in Polyakov's theory of the quantized string

We determine that part of the large-distance correction to the linear potential which is proportional to d, the number of spacetime dimensions. We find that the result depends in a surprising way on the parameter μ which appears in the Liouville theory that results when integrations over string fluctuations have been performed. For μ = 0 the correction is of the expected form $\text{≈?}\text{πd}\text{24}\text{1}\text{R}\text{, (d→?∞, R→∞)}$. However, for any μ ≠ 0 there is no 1/R potential at all with a coefficient proportional to d.     

Supermanifold cohomology and the Wess-Zumino term of the covariant superstring action

The cohomology theory of supermanifolds is developed. Its basic properties are established and simple examples given. The Wess-Zumino term in the Green-Schwarz covariant superstring action is interpreted as a nontrivial class in the supersymmetric cohomology of flat superspace. A quotient supermanifold with nontrivial topology reflecting this class is constructed. It is shown that there is no topological quantization condition for the coefficient of the Wess-Zumino term. The superstring differs from conventional sigma models in this respect because its action is Grassmann-valued and its group manifold (superspace) is noncompact.Enrico Fermi Fellow. Research supported by the NSF (PHY 83-01221) and DOE (DE-AC02-82-ER-40073)