Covariant String Research Articles

The conformal factor and DiffS 1/S 1

Two-dimensional gravity coupled with an open string is considered to geometrically construct a string field theory following Bowick and Rajeev. The phase space of this system can be thought of as an extended loop space, and is in fact a Kähler manifold. Each loop carries a conformal factor. Bowick and Rajeev's proposal is modified so that the ghost fields stand on the same footing as the x μ -fields. The closed string field is modified to be the Kähler potential of the extended loop space. The canonical line bundle is not needed for the equation of motion for a closed string field. A covariant (free) open string field theory is constructed as a by-product in this approach.

The static tachyon potential in the open bosonic string theory

In an effort to understand whether the open bosonic string theory has a stable vacuum, the four-point contribution to the static tachyon potential is computed. This off-shell calculation is carried out using covariant string field theory.

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.

Covariant String Field Theory on Z2-Orbifold

A gauge invariant action is constructed for the closed string compactified on a Z2 -orbifold. Two 3-string vertices which describe two types of interaction, i.e., with and without twisted strings are obtained by the Neumann function method. The O ( g2 ) gauge invariance of the action requires to modify the 3-string vertices by multiplying cocycle factors. A physical interpretation of the cocycle is given.

BRST approach to interacting higher-spin gauge fields

A comprehensive approach to the problem of constructing a consistent classical field theory of interacting higher-spin gauge fields is presented. BRST techniques are used similar to those used in covariant string field theory. A part of the cubic vertex is derived and shown to reproduce the cubic Yang-Mills interaction. Further progress is halted by a lack of an effective way to calculate the full vertex. There are indications that the theory, as presented, might only be consistent in four spacetime dimensions.

A Gauge Invariant Action Containing Both Open and Closed String Fields

An interesting feature of the covariant open string field theory is that the closed string appears as a bound state of the open string.),2) This suggests the existence in open string field theory of a larger gauge symmetry which includes general coordinate transformation. Motivated by this, Hata and N ojiri proposed a new transformation on the open string field) with closed string functional parameter in the formulation of string field theory proposed in Refs. 4) and 5). The structure of the transformation and its algebra are those of stringy general coordinate transformation known in the closed string field theory.5) The gauge invariant open string action is, however, invariant under only the global part of the transformation.. It seems to contradict the existence of the closed string pole in open string one-loop amplitude which is computed from the BRS invariant action. On the basis of a covariant string field theory constructed by Kyoto group,4),5) we propose a new covariant action which contains both open and closed string fields and· is invariant not only under the gauge transformation in the usual open string theory but also under stringy general coordinate transformation. Since the action contains only the interaction terms as in case of the pre-geometrical cubic action in Ref. 6) or Ref. 7), it is background independent. The kinetic term is generated through field condensation of the fields. We investigate the form of the action after the field condensation correspondIng to the flat background. The relation between the new action and the BRS invariant action of Ref. 4) is also discussed in this paper. Before constructing the new action, we define several operations on string fields. First we' define the transition from an open ·string field (j) to a closed string field (denoted by «(j)) and that from a closed string field A to an open string field [A] as follows:*) .

Four-photon scattering amplitude in bosonic open string field theory

The covariant string field theory, which is formulated as a natural generalization of the light-cone gauge approach, is used to calculate three- and four-photon scattering amplitudes explicitly at tree level. The results are found to be consistent with the first quantized covariant approach.

Lie-algebra cohomology and the Osp(1,1‖2) structure in string theory

We construct an improved Becchi-Rouet-Stora-Tyutin (BRST) operator and present generalizations of the standard BRST quantization and the BRST approach to Lie-algebra cohomology. In particular, we show how Lie-algebra two-cocycles can be related to an Osp(1,1\ensuremath{\Vert}2) generalization of the conventional BRST--anti-BRST algebra. As an application we consider open bosonic strings, and explicitly construct the improved BRST operator and the pertinent Osp(1,1\ensuremath{\Vert}2) algebra. We conclude that the string is naturally defined in a (D=28+2)-dimensional Parisi-Sourlas superspace, with phase-space Osp(1,1\ensuremath{\Vert}2) invariance generalized into a spacetime Osp(27,1\ensuremath{\Vert}2) covariance. We construct the Osp(27,1\ensuremath{\Vert}2)-covariant physical string states and establish their equivalence with the conventional D=26 transverse states through a quantum generalization of the Parisi-Sourlas dimensional reduction. We show how the additional two bosonic dimensions emerge from the conventional BRST approach and observe that the ghost number of Osp(1,1\ensuremath{\Vert}2)-invariant physical states vanishes.

String field theory at finite temperature.

We present a real-time formalism enabling us to compute statistical averages of various quantum string field correlation functions and scattering amplitudes in the context of perturbation theory and functional methods. Second quantization of the string fields is carried out in the path-integral representation. Our finite-temperature formalism is a generalization of thermo field dynamics to string field theory for which a doubling of the physical string field degrees of freedom is required. Temperature formally enters our construction by imposing boundary conditions (Kubo-Martin-Schwinger condition) in the generating functional for the string field. Some explicit computations for the case of covariant open bosonic string theory are carried out.

Lorentz Transformation in the Light-Cone Gauge String Field Theory

A complete form of Lorentz transformation law of string field is given explicitly in the light-cone gauge bosonic string field theory. It is shown that the α-symmetry which HIKKO have proved in their covariant string theory in fact implies the Lorentz invariance of the light-cone gauge string field action. We also clarify various properties of the string field products, from which the closure of the Lorentz algebra, for instancem, follows.

On the “Covariantized light-cone” string field theory

We construct a new BRS charge in which the string length parameter and another bosonic parameter are naturally involved as dynamical variables in a string theory. Using the BRS charge we propose another gauge invariant action of covariant string field theory.

Interacting covariant open bosonic strings from the light-cone JI-

BRS gauge-fixed actions for the interacting point particle and bosonic string derived from the light-cone J I- are described. Since J I- for the bosonic string has not previously been found, it is constructed by demonstrating the closure of the Poincaré algebra up to cubic order in string fields.

Covariant heterotic strings and odd self-dual lattices

We investigate the implications of modular invariance for covariantly formulated heterotic strings. It is shown that modular invariant heterotic strings are characterized by odd self-dual lorentzian lattices which include charges of the bosonized superconformal ghosts. The proof of modular invariance involves the anomaly in the ghost number current in a crucial way.

An introduction to covariant superstring field theories

A pedagogical account is given of the recent developments in covariant (super)string field theories. After reviewing the construction of the free open bosonic string field theory, the super-symmetric case is treated and the space-time supersymmetry transformations are explained. The present status and some future problems are also summarized.

Loop amplitudes in covariant string field theory.

The string-length-parameter (\ensuremath{\alpha}) independence of the on-shell physical N-string amplitudes in the covariant string field theory presented by the authors is shown to all loop orders in perturbation theory and for N\ensuremath{\le}d=26. The proof is based on the new invariance of the string action under the field transformation ${\ensuremath{\delta}}^{\ensuremath{\mu}}$\ensuremath{\Phi}=${p}^{\ensuremath{\mu}}$(\ensuremath{\partial}/\ensuremath{\partial}\ensuremath{\alpha})\ensuremath{\Phi}+(${\ensuremath{\Phi}}^{2}$, ${\ensuremath{\Phi}}^{3}$ terms) with ${p}^{\ensuremath{\mu}}$ being the center-of-mass momentum carried by \ensuremath{\Phi}. By making use of this \ensuremath{\alpha} independence, the calculations of the tree and one-loop amplitudes are greatly simplified and shown to reduce directly to the operator formalism expressions. Most remarkably, we find that our pure open-string field theory contains the closed string as a bound state.

Covariant string field theory. II.

The covariant string field theory is presented in its full detail for the closed-bosonic-string case. The properties of the interaction vertex of three closed strings are fully clarified. We thus establish the nilpotency of the full nonlinear Becchi-Rouet-Stora (BRS) transformation as well as the BRS invariance of our gauged-fixed action. This, on the other hand, also establishes the gauge invariance of our gauge-unfixed action and the group law of the gauge transformations, which were reported previously. The general N-point amplitudes for arbitrary external closed-string states are computed explicitly at the tree level. In particular, when the external states are on shell and physical, we prove that the amplitudes become independent of the choice of the external string-length parameters and correctly reproduce the usual dual amplitudes.

Classical gauge and BRST structure of covariant heterotic strings

We investigate the classical world-sheet gauge symmetries of heterotic string theories in the formalism of Siegel, which permits covariant gauge-fixing and BRST quantization. Siegel has demonstrated by algebraic considerations that superstrings possess two further gauge invariances, in addition to the usual general coordinate invariance and the “ k-supersymmetry” discovered by Green and Schwarz. We display the actions of the four gauge symmetries upon all fields, and compute the gauge algebra. The algebra only closes modulo the equations of motion, in principle necessitating arbitrarily complicated ghost interactions in a BRST quantization of the theory. However, the present situation is tractable, and we explicitly display the required BRST structure and ghost interactions.

A new method for constructing gauge string field theory

A new algorithm for constructing covariant gauge string field theory is presented, which is based on the conformal field theory in a general picture for the ghost vacuum. We explain our method in detail by taking the example of the bosonic open string for the case of joining-splitting type 3-string interaction, and show that it reproduces the action constructed by Hata et al. In particular we observe that the ghost prefactor necessary in the 3-string vertex in general is a kind of picture changing operator which pulls “the picture at the interaction point” back to the conformal one. Our method is generated and is applicable also to Witten's type of mid-point interaction and to superstring field theories. We can construct an action based on any pictures of ghost vacua.

A four-dimensional string

From a modified Green-Schwarz covariant supersymmetric string action, we construct a free four-dimensional string. The new theory is tachyon-free, ghost-free and Lorentz invariant. And the spectra possess “supersymmetric property”.

Covariant fermionic and heterotic strings from the bosonic string

We discuss the embedding of the covariantly formulated superstring and heterotic string theories into the 26-dimensional bosonic string. The construction is based on equalities among bosonic and fermionic one-loop partition functions and, in particular, shows how the one-loop partition function of the superconformal ghost system can be obtained from the compactified bosonic string. It provides a natural expression for the covariant fermion vertex operator in the context of the bosonic string. We also discuss the necessary truncations which are needed to obtain the covariant heterotic string by compactification of the bosonic string on self-dual lattices.